Multi-stage parallel super-high-speed ADC and DAC of logarithmic companding law

ABSTRACT

Multi-stage parallel super-high-speed ADC and DAC of a logarithmic companding law has a voltage follower switch having zero voltage drop, and also has a lossless threshold switch group, wherein a quantization voltage of A/D conversion or D/A conversion is directly obtained through voltage-dividing resistance thereof. The ADC and DAC simplify a conversion process and reduce a conversion error. The ADC and DAC provide multi-stage multi-bit parallel super-high-speed A/D conversion and D/A conversion with logarithmic companding law of a high conversion rate and the low conversion error.

CROSS REFERENCE OF RELATED APPLICATION

This is a U.S. National Stage under 35 U.S.C 371 of the International Application PCT/CN2013/000173, filed Feb. 22, 2013, which claims priority under 35 U.S.C. 119(a-d) to CN 201110440575.1, filed Dec. 26, 2011; CN 201210185940.3, filed May 30, 2012; and CN 201310048568.6, filed Feb. 7, 2013.

BACKGROUND OF THE PRESENT INVENTION

1. Field of Invention

The present invention relates to digital communications, and more particularly to an Analog-to-Digital Converter (ADC) and a Digital-to-Analog Converter (DAC).

2. Description of Related Arts

According to the theoretical analysis, for the communications system, the logarithmic compression law is most ideal but difficult to realize. Conventionally, the communications system employs the companding codes. For example, the audio communications employs the 8-bit companding codes of the A-compression-law and the μ-compression-law whose signal-to-noise ratio (SNR) curves are respectively showed as 1 and 2 in FIG. 1.3, wherein the SNR curves thereof are only approximations to the logarithmic compression law, not ideal SNR curves. Then what shape is the ideal SNR curve supposed to have? The ideal SNR curve satisfies that the SNR does not change with the analog input signal amplitude and the probability density distribution; in other words, the ideal SNR curve is supposed to be a horizontal line 3 as a constant. Furthermore, the ideal SNR curve is supposed to move up and extend right as much as possible, wherein moving the curve up means increasing the SNR and extending the curve right means broadening the signal dynamic range.

Conventionally, the circuit for accomplishing the companding coding is the successive approximation ADC which is slower than the parallel ADC by two orders of magnitude. However, the conventional parallel ADC is unable to accomplish the ideal companding coding. Thus, it becomes the object of the present invention to provide a parallel ADC capable of accomplishing the logarithmic compression law and a correspondent DAC of the logarithmic expansion law.

According to the present invention, the Analog-to-Digital (AD) conversion having a constant SNR is theoretically analyzed as follows.

Firstly, a method for stabilizing an SNR of an ADC at a constant is deduced; a value of the SNR and a signal dynamic range are counted. Given that: a probability density distribution is P(u); when V_(j−1)<u≦V_(j) (j=1 . . . Q), a quantizer inputs a signal power S_(j) and a noise power is N_(j); ΔV_(j)=V_(j)−V_(j−1), wherein a quantizer step size of axis V, ΔV_(j), is a variable; V_(j−1) is temporarily taken as a quantized point of u for the analysis, signal average power of u: S _(j)=∫_(v) _(j−1) ^(V) ^(j) u ² P(u)du  (1.1); noise average power of u: N _(j)=∫_(V) _(j−1) ^(V) ^(j) (u−V _(j−1))² P(u)du  (1.2); SNR: S _(j) /N _(j)=∫_(V) _(j−1) ^(V) ^(j) u ² P(u)du/[∫ _(V) _(j−1) ^(V) ^(j) (u−V _(j−1))² P(u)du]  (1.3).

Because V₀˜V_(P) is divided into Q subzones, ΔV_(j) is small enough and thus P(u) in the interval ΔV_(j) is equal to a constant. Substituted with V_(j)=V_(j−1)+ΔV_(j) and X=V_(j−1)/ΔV_(j), the SNR is simplified as: S _(j) /N _(j) =P(u)∫_(V) _(j−1) ^(V) ^(j) u ² du/[P(u)∫_(V) _(j−1) ^(V) ^(j) (u−V _(j−1))² du]=(3V ² _(j−1) *ΔV _(j)+3V _(j−1) *ΔV ² V _(j)+Δ³ V _(j))/Δ³ V _(j)=3(X ² +X+1/3)=3(X+1/2)²+1/4;  (1.4.1) [S _(j) /N _(j)]_(dB)=10 log(3(X+1/2)²+1/4)≈10 log 3+20 log(V _(j−1) /ΔV _(j)+1/2)  (1.5.1)

If equaling V_(j)/ΔV_(j) to a constant, the value of S_(j)/N_(j) becomes a constant and the object of stabilizing the SNR [S_(j)/N_(j)]_(dB) at the constant is accomplished, wherein the [S_(j)/N_(j)]_(dB) maintains constant in a range of 20 log V_(P)/V_(P)˜20 log V_(θ)/V_(P); in other words, the dynamic range of [S_(j)/N_(j)]_(dB) is 0˜20 log V_(θ)/V_(P). As showed in FIG. 1.4, given that V_(θ)=u_(θ), wherein u_(θ) is a minimal effective signal which a sensor is able to obtain, u is at a signal dead zone when u is at a range of (V_(θ)˜0); then let the sensor signal u=0 and be merged into a zone y₀, S_(j)/N_(j)=0.

Then the quantized point is processed with a half-step quantization. In order to determine quantization resistances R_(θ)˜R_(Q), V_(j−1) is temporarily taken as the quantized point. Once R_(θ)˜R_(Q) are determined, the quantized point is adjusted into a real quantized point U_(j−1)=(V_(j−1)+V_(j))/2. U_(j−1) is named as a half-step quantized point, and an integral interval of N_(j) is changed and ranges from U_(j−1)−ΔV_(j)/2 to U_(j−1)+ΔV_(j)/2, namely the quantization step size after adjusting the quantized point becomes ΔU_(j), wherein ΔU_(j)=ΔV_(j)/2. With identical original data, a quantization error decreases ¾ and [S_(j)/N_(j)]_(dB) increases 10 log 4=6.02 dB. Here comes the question about how to adjust the quantized point. In the AD conversion process, adjusting the quantized point complicates the circuit; moreover, information after the AD conversion becomes digital, which means it is impossible to adjust the quantized point. Thus the Digital-to-Analog (DA) conversion permits adjusting the quantized point; in other words, during the DA conversion process, the quantized point V_(j−1) is adjusted into U_(j−1)=(V_(j−1)+V_(j))/2. ΔU_(j)=ΔV_(j)/2, substituted with V_(j)=V_(j−1)+ΔV_(j) and then X=V_(j−1)/ΔV_(j), the SNR is simplified as: S _(j) /N _(j) =P(u)∫_(U) _(j−1) _(−ΔU) _(j) ^(U) ^(j−1) ^(+ΔU) ^(j) u ² du/[P(u)∫_(U) _(j−1) _(−ΔU) _(j) ^(U) ^(j−1) ^(+ΔU) ^(j) (u−U _(j−1))² du]=[u ³|_(U) _(j−1) _(−ΔU) _(j) ^(U) ^(j−1) ^(+ΔU) ^(j) ]/[(u−U _(j−1))³|_(U) _(j−1) _(−ΔU) _(j) ^(U) ^(j−1) ^(+ΔU) ^(j) ]=3[((V _(j−1) +V _(j))/2)/(ΔV _(j)/2)]²+1=3[((2V _(j−1) +ΔV _(j))/2)/(ΔV _(j)/2)]²+1=12(X+1/2)²+1=4[3(X+1/2)²+1/4];  (1.4.2) [S _(j) /N _(j)]_(dB)=10 log 4(3(X+1/2)²+1/4)≈10 log 12+20 log(V _(j−1) /ΔV _(j)+1/2)  (1.5.2)

(1.4.2) is four times of (1.4.1); (1.5.2)=(1.5.1)+10 log 4.

Secondly, how to set V_(j) and ΔV_(j), i.e., how to determine the value of each quantized point V_(θ), V₁ . . . V_(Q−1), is analyzed. The value of each quantized point depends on a resistance of each resistor in a resistor chain, so a rule about how to set the resistance is simultaneously inferred.

Inference 1: If V_(j)/ΔV_(j)=a constant, the value of each quantized point V_(θ), V₁ . . . V_(Q) geometrically increases, namely V ₁ =V _(θ)*η¹ ,V ₂ =V _(θ)*η² . . . V _(Q−1) =V _(θ)*η^(Q−1) ,V _(P) =V _(θ)*η^(Q);  (1.6) Proof: Since ΔV _(j) /V _(j)=(V _(j+1) −V _(j))/V _(j)=(V _(j+1) /V _(j))−1=a constant  (1.7) V _(j+1) /V _(j)=η (η is a geometric constant)  (1.8) Then V ₁ /V _(θ) =V ₂ /V ₁ = . . . =V _(Q−1) /V _(Q−2) =V _(P) /V _(Q−1)=η  (1.9)

Thus V₁, V₂ . . . V_(Q−1) are respectively: V₁=V_(θ)*η¹, V₂=V_(θ)*η² . . . V_(Q−1)=V_(θ)*η^(Q−1), V_(P)=V_(θ)*η^(Q)

Consequently, Conclusion 1: if the value of each quantized point geometrically increases on the basis of potential V_(θ), the SNR becomes constant, which means the logarithmic law of compression and expansion are accomplished.

Inference 2 is obtained as a result of the Inference 1.

Inference 2: In order to satisfy a requirement that the value of each quantized point V_(θ), V₁ . . . V_(Q) geometrically increases, it must be given that {circle around (1)}R ₁ /R _(θ)=η−1  (1.10); {circle around (2)}R _(j+1) /R _(j)=η(j=1 . . . Q−1)  (1.11);

wherein R₁, R₂ . . . R_(Q) are respectively: R₁=R_(θ)*(η−1), R₂=R₁*η¹, R₃=R₁*η² . . . R_(Q)=R₁*η^(Q−1).

Deduction {circle around (1)}: Since V₁=V_(θ)*η, I(R₁+R_(θ))=I*R_(θ)*η, then R₁/R_(θ)=η−1;

Deduction {circle around (2)}: R_(θ)+ . . . +R_(j) is simply marked as ΣR_(j); according to the equation (1.8), V_(j+1)=V_(j)*η, namely I*ΣR_(j+1)=I*ΣR_(j)*η, then ΣR_(j+1)−ΣR_(j)=ΣR_(j)*η−ΣR_(j), R_(j+1)=ΣR_(j)*(η−1), R_(j+1)/ΣR_(j)=η−1; also then R_(j)/ΣR_(j−1)=η−1; thus R_(j+1)/R_(j)=ΣR_(j)/ΣR_(j−1)=(R_(j)+ΣR_(j−1))/ΣR_(j−1)=R_(j)/ΣR_(j−1)+ΣR_(j−1)/ΣR_(j−1)=(η−1)+1=η; Q.E.D.

Consequently, Conclusion 2: On the basis of the resistance R_(θ), given that R₁/R_(η)=η−1 and R_(j+1)/R_(j)=η, wherein η is given a range of (1.001˜1.5) in the present invention, V_(j+1)/V_(j)=η; the SNR becomes constant, so that the logarithmic law of compression and expansion are accomplished.

Since V_(P) is known, once two of V_(θ), Q and η are determined, the rest one can be determined via deduction. In most cases, V_(θ) and Q are determined firstly to compute the correspondent η, V₁˜V_(Q−1) and R_(θ)˜R_(Q−1).

Conventionally, the audio communications employs the 8-bit digital signals, wherein one bit is for indicating positive or negative and other seven bits are for coding, in such a manner that Q=2^(q)=128, which requires the dynamic range to be no less than 40 dB and the SNR to be no less than 26 dB. As a design of the constant SNR according to the present invention, supposing that V_(P)=10000Δ, wherein Δ is a uniform quantization unit, as showed in Table 1, the SNRs, [S_(j)/N_(j)]_(dB), and the signal dynamic ranges of V_(θ)=10 Δ, V_(θ)=5Δ, V_(θ)=2Δ, V_(θ)=1Δ and V_(θ)=0.1Δ are respectively counted according to the equation (1.5.2). Further referring to FIG. 1.5, let a basic potential equal to a potential of the signal dead zone V_(θ), if the weak signal zone employs a high SNR, the signal dead zone V_(θ) is one order of magnitude larger than the few initial quantization steps ΔV₁, ΔV₂, ΔV₃ . . . , which causes a waste of resource; thus it is necessary for V_(θ) to be at identical order of magnitude with ΔV₁, ΔV₂, ΔV₃ . . . to reduce the signal dead zone, despite of a fact that the SNR within the weak signal zone decreases to some extent. Actually, within the weak signal zone, the signal devices are supposed to focus on detecting and converting. For example, for the weak signals, the radar focuses on finding the target objects as early as possible, when the SNR is allowed to be reasonably low. The SNR increases rapidly along with the strengthened signals; within the medium and strong signal zones, the high SNR is required. The above arrangement of the parameter balances the two features, the SNR [S_(j)/N_(j)]_(dB) and the signal dynamic range, to a limit level.

TABLE 1 (V_(p) = 10000Δ; Q = 128) V_(θ) η [S_(j)/N_(j)]_(dB) dynamic range  10Δ 1.05545 36.15 60   5Δ 1.06118 35.32 66   2Δ 1.0688 34.33 74   1Δ 1.07461 33.65 80 0.1Δ 1.09411 31.72 100

An example is listed as follows to illustrate how to accomplish the design of the present invention. Firstly, setting all of the quantized points V_(θ)˜V_(Q−1) and determining the quantization resistances R_(θ)˜R_(Q) based on the parameters listed at the first line of Table 1, wherein the SNR [S_(j)/N_(j)]_(dB)=36.15 but the signal dead zone V_(θ)=10Δ is one order of magnitude larger than the quantization step size ΔV₁=0.05545Δ, which causes the waste of resource; secondly, adjusting the signal dead zone V_(θ)=10Δ into V^(#) _(θ)=V_(θ)/10=1Δ, namely letting R^(#) _(θ)=R_(θ)/10, in such a manner that the post-adjusting signal dead zone V^(#) _(θ)=1Δ and the quantization step size ΔV₁=0.05545Δ are at the identical order of magnitude, which greatly reduces the signal dead zone; thirdly, computing the SNR to obtain Table 2 based on the post-adjusting equation [S _(j) /N _(j)]_(dB)=10 log 4(3(X+1/2)²+1/4)≈10.792+20 log(V ^(#) _(j−1) /ΔV _(j)+1/2)  (1.5.3),

wherein it is confirmed that the minimal SNR is within an available range, as well as that the SNR increases rapidly with the strengthening of the signal and quickly gets close to the maximum value 36.15. The dynamic range including the section of low SNR expands into 80 dB after the adjusting from the previous 60 dB, as showed in Table 2.

TABLE 2 V_(θ) = 10Δ; η = 1.05545; V^(#) _(θ) = 1Δ; [S_(j)/N_(j)]_(dB) = 36.15 dB; dynamic range = 80 dB j V_(j−1) ΔV_(j) V^(#) _(j−1) V^(#) _(j−1)/ΔV_(j) [S_(j)/N_(j)]_(dB) 1 10.00 0.555 1.000 1.803 18.04 2 10.55 0.585 1.555 2.656 20.78 3 11.14 0.618 2.140 3.464 22.75 4 11.76 0.652 2.757 4.230 24.29 5 12.41 0.688 3.409 4.955 25.53 6 13.10 0.726 4.097 5.462 26.56 7 13.82 0.767 4.824 6.293 27.43 8 14.59 0.809 5.590 6.910 28.19 9 15.40 0.854 6.399 7.494 28.85 10 16.25 0.901 7.253 8.048 29.43 11 17.15 0.951 8.154 8.573 29.95 12 18.11 1.004 9.11 9.07 30.41 13 19.11 1.060 10.11 9.54 30.83 14 20.17 1.118 11.17 9.99 31.20 15 21.29 1.180 12.29 10.41 31.55 16 22.47 1.246 13.47 10.81 31.86 The following are some illustrations about the present invention.

-   -   The multi-stage parallel super-high-speed ADC and DAC of the         logarithmic companding law, provided by the present invention,         are respectively simplified as the logarithmic ADC and the         logarithmic DAC; the logarithmic ADC and the logarithmic DAC         together are named as the logarithmic ADDA; sub-stages of the         logarithmic ADC, the logarithmic DAC and the logarithmic ADDA         are respectively simplified as sub-ADC, sub-DAC, sub-ADDA; two         and more than two sub-stages are defined as multi-stage; the         logarithmic ADDA comprises the multi-sub-ADDAs; AD##, DA##,         A##D, AD#, DA# and A#D are respectively symbols of the         logarithmic ADC, the logarithmic DAC, the logarithmic ADDA, the         sub-ADC, the sub-DAC and the sub-ADDA.     -   λ is a wildcard character substituted for α, β, γ . . . ; in         order to avoid conflicts of numbering, α, β, γ . . . actually         represent 1, 2, 3 . . . ; stage α, stage β, stage γ . . .         respectively represent stage 1, stage 2, stage 3 . . . , wherein         stage m is the last stage; stage λ has a conversion bit of         q_(λ); μ=λ+1 represents the next stage of λ.     -   Stage α is the top stage, namely the stage α corresponds to the         highest q_(α) bit of N-bit binaries; the bit numbers         respectively correspondent to stage β, stage γ . . . decrease         successively; for example, N=4 stages*3 bits=12 bits; the three         bits, D_(α2)D_(α1)D_(α0), of stage α correspond to the highest         D₁₁D₁₀D₉ bit; the three bits, D_(β2)D_(β1)D_(β0), of stage β         correspond to the second high D₈D₇D₆ bit . . . .     -   The stage-potential switch JDWKG comprises the multi-channel         switches DLKG and the threshold switches LJKG. The two types of         switches are equivalent, so any illustration about the one type         applies to the other type.     -   For the logarithmic ADC, the alternating analog voltage signal,         represented by the lowercase u_(αy), only appears before the         front-end circuit at the stage α; U_(λy) represents the positive         fluctuating analog voltage signal inputted at the stage λ which         is simplified as the input voltage U_(λy) thereafter; the         inputted voltage U_(λy) is converted into the stage-potential         V_(λG), and then the stage-potential V_(λG) is converted into         the digital signal D_(λ(q−1)) . . . D_(λ0) wherein the         stage-potential V_(λG) works as a bridge.     -   For the logarithmic DAC, the digital signal at the stage λ         D_(λ(q−1)) . . . D_(λ0) is converted into the stage-potential;         through proportional attenuation, the stage-potential becomes         the outputted positive analog voltage signal, or the output         voltage for short.     -   The input voltage and the output voltage together are called the         analog voltage.     -   Hereafter, the sub-stage all-parallel ADC is called the         parallelizer for short; the sampling/holding device is called         the sampler/holder CB for short.     -   The specifically embodied circuits are various, and the circuit         illustrated in the present invention is only exemplary.     -   The nature of the symbol remains regardless of the subscripts;         for example, CB is the sampler/holder and CB_(β) is still the         sampler/holder, wherein the subscript β is only the stage         footnote; the subscript (Q−1)˜0 represents step (Q−1)˜step 0;         the subscript (T−1)˜0 represents step (T−1)˜step 0; the         subscript (q−1)˜0 represents bit (q−1)˜bit 0; the subscript         (t−1) represents bit (t−1)˜bit 0; the subscripts α, β and γ         represent the stage, and λ is the wildcard character for each         stage.     -   The circuit within the solid frame or the dashed frame is the         module whose name is provided at the corner.     -   The control characters I*_(λg) and I_(λg) are connected with         wires, i.e., I*_(λg)=I_(λg); thus I*_(λg) and I_(λg) refer to         the same control character; I_(λg) is showed at the output         terminal of the comparator, and I_(λg) is showed at the control         terminal of the threshold switch.     -   If the defined symbol, such as V₁, is given a renewed         definition, the symbol represents the renewed definition         thereafter.     -   The voltage follower, abbreviated as follower, is the integrated         operational amplifier (integrated op-amp) having the short         connection of the inverting input terminal (abbreviated as the         inverting terminal) and the output terminal. One skilled in the         electronics understands that the signal is inputted via the         non-inverting input terminal (abbreviated as the non-inverting         terminal) and that the voltage of the output terminal accurately         follows and equals the inputted signal. In other words, the         voltage drop of the signal voltage from the input terminal to         the output terminal is extremely small (smaller than 10⁻⁸V);         technically speaking, the voltage drop is zero, or the         on-resistance is zero. Meanwhile, the input resistance is         extremely larger (as large as 10⁹Ω); technically speaking, the         input resistance is infinitely great. The follower is         represented by a triangle without any number.     -   The input signal voltage and the output signal voltage of the         voltage follower switch, or the follower switch for short, have         the effective intervals. All the signal voltages mentioned in         the present invention are within the effective intervals. The         follower switch has various logic relations, and the threshold         switch is one type of the follower switch.     -   The threshold switch S_(λg) represents the threshold switch at         the step g, stage λ. S_(λg) has the upper control character         I_(λ(g+1)) and the lower control character I_(λg). The step         number at each stage can be different; the variable symbol of         the step number at each stage is uniformly represented by g,         only for convenience.     -   In order to simplify the illustration, the present invention         makes following appointments. The reference points         V_(λ(Q−1))˜V_(λ1) are correspondently connected to the inverting         terminals of the comparators C_(λ(Q−1))˜C_(λ1); the         to-be-compared analog voltage U_(λZ), or the to-be-compared         voltage for short, are connected to the non-inverting terminals         of the comparators C_(λ(Q−1))˜C_(λ1); the positive logic is         adopted, wherein “1” represents that U_(λZ) is higher than the         reference voltage and “0” represents that U_(λZ) is lower than         the reference voltage; for example, supposing that the stage λ         has a threshold point G, for the to-be-compared voltage at stage         λU_(λZ)>(V_(λG)˜V_(λ0)), the control characters I_(λG)˜I_(λ0)         correspondent to the reference points V_(λG)˜V_(λ0) are equal to         1; and for U_(λZ)<(V_(λQ)˜V_(λ(G+1))), the control characters         I_(λG)˜I_(λ(G+1)) correspondent to the reference points         V_(λG)˜V_(λ(G+1)) are equal to zero. The opposite appointment is         also acceptable.

SUMMARY OF THE PRESENT INVENTION

Multi-stage parallel super-high-speed ADC and DAC of a logarithmic companding law have a characteristic of a logarithmic ADDA comprising multi-sub-ADDAs, wherein at least one sub-ADDA comprises a stage-potential processing device, wherein the stage-potential processing device at stage λ comprises two general modules.

The first general module is a potential generating module at stage λ which comprises a resistor chain for generating reference potential points and a stage-potential determining circuit. Let Q=2^(q), the reference potential points of the sub-ADDA at stage λ bit q are formed by series connected Q resistors; the resistor chain of the series connected Q resistors forms Q+1 potential points V_(λQ), V_(λ(Q−1)) . . . V_(λ1), V_(λ0), among which V_(λ(Q−1)) . . . V_(λ1), V_(λ0) are the reference potential points at step Q stage λ, wherein V_(λQ) is equal to V_(p) at a power source anode, and is excluded from the reference potential at step Q. Let g equal to some point whose step subscript is within (0˜Q−1), point g is called a test point, and V_(λg) is called the reference potential at step g stage λ. A quantization distance, also called a step difference, Δ_(λg)=V_(λ(g+1))−V_(λg); when a to-be-compared voltage U_(λZ) falls within a conversion range V_(λQ)˜0, there is always a point G correspondent to U_(λZ), wherein, when g=G, V_(λ(G+1))>U_(λZ)>V_(λG) and U_(λZ)−V_(λG)<Δ_(λG). Particularly, point G is named as a stage point, and V_(λg) at the stage point G is the reference point which is smaller than and closest to U_(λZ) and is a special reference point among the reference points V_(λ(Q−1))˜V_(λ0), especially marked as V_(λG) which is a stage-potential at stage λ. Relative to the sub-ADDA at stage λ, the stage-potential V_(λG) is a conversion value of U_(λZ). The stage-potential V_(λG) is actually a bridge between the to-be-compared voltage U_(λZ) at stage λ and digital signals D_(λ(q−1)) . . . D_(λ0) at stage λ; the stage-potential V_(λG) corresponds not only to digitals, but also to analogs, and is a digitized analog value. Taken a further consideration, there exists a problem that it is wrong to express the stage point of each stage with g and G, because the test point of each stage among m sub-stages is independent, and thus the stage point of each stage can be different. In order to simplify illustration of the present invention, the present invention makes following appointments: at stage α, β, γ, δ . . . , the test points are respectively represented by a, b, c, d . . . , and the stage points are respectively represented by A, B, C, D . . . ; g is a wildcard character substituted for the symbol of each test point, so g is a wildcard of the test point; G is a wildcard character substituted for the symbol of each stage point, so G is the wildcard of the stage point; without misunderstanding, the wildcard characters g and G are uniformly used to illustrate principles.

The second general module is a stage-potential extracting module. For the sub-ADDA at stage λ, although it can be determined that which of the reference potential points V_(λ(Q−1))˜V_(λ0) is the stage-potential V_(λG), the stage-potential V_(λG) still remains to be extracted, which requires the stage-potential extracting module. The stage-potential extracting module is a stage-potential switch. A group of threshold switches forms the stage-potential switch. The stage-potential switch JDWKG_(λ) comprises a threshold switch group LJKGZ_(λ) and a multi-channel switch DLKG_(λ), wherein the threshold switch group is the group of the threshold switches whose output terminals are parallel connected into a common terminal and whose input terminals form an input terminal group of the threshold switch group. Control characters are provided for directly choosing and connecting one of the input terminals as a strobe terminal. The threshold switch S_(λg) at step g stage λ has an upper control character I_(λ(g+1)) and a lower control character I_(λg). Table 3 shows logic relations among S_(λg), I_(λ(g+1)) and I_(λg).

TABLE 3 logic of S_(λg) I_(λg) I_(λ(g+1)) S_(λg) 0 0 OFF 0 1 OFF 1 0 ON 1 1 OFF

The threshold switch group has a strobe control as follows. Firstly, let I_(λQ)≡0 and I_(λ0)≡1, the upper and the lower control characters I_(λ(g+1)) and I_(λg) of S_(λg) are respectively connected to and equal to potential comparison values I*_(λ(g+1)) and I_(λg); when I_(λ(g+1))=1 or I_(λg)=0, the switch point S_(λg) is disconnected; only when the switch point S_(λg) satisfies the requirements of I_(λ(g+1))=0 and I_(λg)=1, namely the switch point S_(λg) is at a threshold point G having the upper control character “0” and the lower control character “1”, the switch point S_(λg) is connected and becomes a strobe point S_(λG). A potential at the strobe point S_(λG) is a potential at step G stage λ, V_(λG); V_(λG) is called the stage-potential of stage λ.

The stage-potential V_(λG) is a bridge of A/D conversion and D/A conversion, and corresponds respectively to the digital signals D_(λ(q−1))˜D_(λ0) and the to-be-compared voltage U_(λZ), wherein the corresponding is accomplished via a correspondence between the reference points V_(λ(Q−1))•V_(λ0) and the control characters I_(λ(Q−1))˜I_(λ0), and a correspondence between the reference points V_(λ(Q−1))˜V_(λ0) and the threshold switch group S_(λ(Q−1))˜S_(λ0). The stage-potential V_(λG) is a threshold point among the reference points V_(λ(Q−1))˜V_(λ0), and is determined through values of the control characters I_(λ(Q−1))˜I_(λ0) and the strobe terminal of the threshold switch group S_(λ(Q−1))˜S_(λ0).

The stage-potential V_(λG) is obtained through the correspondence between the reference points V_(λ(Q−1))˜V_(λ0) and the control characters I_(λ(Q−1))˜I_(λ0), and the correspondence between the reference points V_(λ(Q−1))˜V_(λ0) and the switch group S_(λ(Q−1))˜S_(λ0).

Firstly, the correspondence between V_(λ(Q−1))˜V_(λ0) and the digital signals, or the correspondence between V_(λ(Q−1))˜V_(λ0) and the control characters I_(λ(Q−1))˜I_(λ0) which convert into the digital signals, is illustrated as follows. Since “1” represents that the to-be-compared voltage is higher than the reference point voltage; among the reference points V_(λ(Q−1))˜V_(λ0), V_(λG) is the threshold point, when the to-be-compared voltage at stage λ U_(λZ)>(V_(λG)˜V_(λ0)), the control characters I_(λG)˜I_(λ0) correspondent to the reference points V_(λG)˜V_(λ0) are equal to 1; in other words, each threshold switch (S_(λ(G−1))˜S_(λ0)) connected below V_(λG) (g=0˜(G−1)) has the control character I_(λ(g−1))=I_(λg)=1, so (S_(λ(G−1))˜S_(λ0)) are at states of OFF in Table 3; when U_(λz)<(V_(λQ)˜V_(λ(G+1))), the control characters I_(λQ)˜I_(λ(G+1)) correspondent to the reference points V_(λQ)˜V_(λ(G+1)) are equal to zero; in other words, each threshold switch (S_(λ(G+1))˜S_(λ(Q−1))) connected above V_(λG) (g=(G+1)˜(Q−1)) has the control character I_(λ(g+1))=I_(λg)=0, so (S_(λ(G+1))˜S_(λ(Q−1))) are at states of OFF too; only when the threshold switch S_(λG) at the threshold point G has the control characters I_(λ(G+1))=0 and I_(λG)=1, S_(λG) is at a state of ON in Table 3. Secondly, V_(λ(Q−1))˜V_(λ0) and the correspondent S_(λ(Q−1))˜S_(λ0) are connected directly, or correspondently (which means one-to-one via an arithmetic circuit). The strobe point S_(λG) among S_(α(Q−1))˜S_(λ0) extracts out the stage-potential V_(λG), or a stage output value via an operation on V_(λG), sends the extracted stage-potential V_(λG) into a main line S_(λ) of the stage-potential switch; the sent stage-potential V_(λG) and the stage output values of other sub-ADDAs are collected and calculated, for accomplishing the A/D and D/A conversions. The so-called stage-potential V_(λG) is the reference point potential closest to the to-be-compared voltage U_(λZ); V_(λG) and U_(λZ) have a relation of: V_(λG)=U_(λZ)−U_(λx), wherein U_(λx) is a residue voltage which is smaller than a span of the reference point voltage.

The multi-channel switch is a threshold switch group in essence, except that the control characters of the multi-channel switch are formed by decoding the digital signals; in other words, the multi-channel switch comprises a decoder and a threshold switch, wherein firstly the digital signals are decoded into the control characters by the decoder, and then one switch point of the threshold switch group is chosen and connected to be a strobe point through the control characters. The threshold switch group and the multi-channel switch are equivalent and alternative, and are generally called the stage-potential switch.

The threshold switch comprises the conventional switch having a signal loss, and a lossless threshold switch, or a lossless switch for short, provided by the present invention. The lossless switch comprises a voltage follower switch (follower switch) which functions as a signal switch for transmitting or blocking signals, wherein the voltage follower switch comprises two modules, a module of a voltage follower (follower) and a module of a power source loop switch (power source switch). The power source switch is an electronic device provided on an operational power source loop (power source loop) of the follower; connection and disconnection of the power source loop of the follower is controlled by the control characters, so as to control connection and disconnection of a signal loop of the follower.

These and other objectives, features, and advantages of the present invention will become apparent from the following detailed description, the accompanying drawings, and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1.1 is a sketch view of a threshold switch according to Embodiment 1.1 of the present invention, wherein subscript λg represents step g stage λ; rectangular block S_(λg) is a threshold switch at step g stage λ; V_(λg) is a signal point at step g stage λ; I_(λg) is a control character at step g stage λ; V_(λ(g+1)) is a control character at step g+1 stage λ; S_(λ) is a switch main line at stage λ; V_(λg) is a potential of the main line at stage λ.

FIG. 1.2.1 is a schematic diagram of a lossless switch type S_(λg1) according to Embodiment 1.2.1 of the present invention, wherein A_(λg) is a follower; V_(λg), l_(λg), I_(λ(g+1)), S_(λ) and V_(λG) are identical to those showed in FIG. 1.1; VT1 and VT3 are NPN transistors; VT0 and VT2 are PNP transistors; +V_(P) is an anode of a power source and −V_(N) is a cathode of the power source; a circuit within a dashed frame forms the lossless threshold switch S_(λg1).

FIG. 1.2.2 is a schematic diagram of a lossless switch type S_(λg2) according to Embodiment 1.2.2 of the present invention, wherein A_(λg), V_(λg), I_(λg), I_(λ(g+1)), S_(λ), +V_(P) and −V_(N) are identical to those showed in FIG. 1.2.1; VT4 to VT9 are all NPN transistors; V_(5C) and V_(8C) are respectively potentials of collector terminals of VT5 and VT8; R_(λ) is a resistor; a circuit within a dashed frame forms the lossless threshold switch S_(λg2).

FIG. 1.2.3 is a schematic diagram of a lossless switch in broad sense type S_(λg3) according to Embodiment 1.2.3 of the present invention, wherein KS1 and KS3 are power source switches conducting at high potential; KS0 and KS2 are power source switches conducting at low potential.

FIG. 1.2.4 is a schematic diagram of a q-bit multi-channel switch according to Embodiment 1.2.4 of the present invention, wherein S_(λ0)˜S_(λ(Q−1)) are the threshold switches at steps 0˜(Q−1) stage λ; a solid frame LJKGZ_(λ) is a threshold switch group at stage λ; V_(λ0)˜V_(λ(Q−1)) are potentials of input terminals at steps 0˜(Q−1) stage λ; I_(λ0)˜I_(λQ) are control characters at steps 0˜(Q−1) stage λ; d_(λ0)˜d_(λ(q−1)) are control terminals of the multi-channel switch at stage λ; JM_(λ) is a decoder; a dashed frame DLKG_(λ) represents the multi-channel switch.

FIG. 1.3, FIG. 1.4 and FIG. 1.5 are referred in the theoretical analysis about the AD conversion having a constant SNR.

FIG. 1.3 is a diagram of SNR curves of 7-bit companding codes respectively of A-compression-law, μ-compression law and a logarithmic compression law, wherein SNR curve of A-compression-law-1; SNR curve of μ-compression law-2; SNR curve of logarithmic compression law having a constant SNR-3; SNR curve of logarithmic compression law having an adjusted SNR-4.

FIG. 1.4 is a sketch view of a q-bit all-parallel ADC, wherein Q=2^(q); Q is a quantization step number; V_(θ) is a base potential point, and V₁ is a start potential point; V_(θ) is V₀; in order to distinctly differ from other potential points, V₀, a key potential point, is represented by V_(θ); similarly, R_(θ) is a base resistance and R₁ is a start resistance; V_(θ) and V₁˜V_(Q−1) are potential reference points which are dependent on a determination of resistances of the resistors R_(θ)˜R_(Q); the resistances of the resistors R_(θ)˜R_(Q) are determined according to practical needs; u is an analog input signal; C₁˜C_(Q−1) are comparators; BMQ is an encoder for encoding Q states of Y₀˜Y_(Q−1) into q-bit binaries D₀˜D_(q−1); common symbols, such as V_(p), an anode of a power source, and a ground terminal, are also used in following drawings, without repeating explanation again.

FIG. 1.5 is a partial view of compression characteristics, wherein Q−1 quantized points V_(A) V₂ . . . V_(Q−1) are inserted between V_(θ) and V_(P) on axis V at a geometric V_(j+1)/V_(j)=η interval, as well as V_(θ) and V_(Q)=V_(P), which means that totally Q+1 quantized points are inserted to divide the interval from V_(θ) and V_(P) into Q sub-intervals to form Q segments; Q+1 coordinate points (y₀˜y_(Q)) which are drew on axis Y at evenly spaced intervals, correspond to the digital values and also correspond to the evenly spaced analog values, Q line segments. Let a correspondence between V and y of the compression curve be: (V₁˜V_(θ)˜0)→y₀, (V₂˜V₁)→y₁, (V₃˜V₂)→y₂, . . . (V_(Q)˜V_(Q−1))→y_(Q−1), V_(Q)→y_(Q), since y₀₊ and y⁰⁻ overlap at an origin point, the positive Q sub-intervals and the negative Q sub-intervals are integrated into 2*Q−1 sub-intervals.

For facilitating reading, view numbers of following drawings are set to be correspondent to embodiment numbers on purpose. The drawings are illustrated in the correspondent embodiments. The drawings and the correspondent embodiments are combined and illustrated. Like reference characters in the drawings indicate corresponding elements throughout the several views, unless being further explained. The subscript λg represents step g stage λ.

FIG. 2.1A is an enlargement view of part A of FIG. 2.1; FIG. 2.1B is an enlargement view of part B of FIG. 2.1.

FIG. 2.1 is a schematic diagram of m stages*3-bit equal resistance type logarithmic ADC according to Embodiment 2.1 of the present invention, wherein λ is a wildcard character substituted for α, β, γ and m; u_(αy) is an original input alternating signal; QZDL is a front-end circuit; AD#_(λ) is an A/D conversion sub-module at stage λ of the ADC; AD#_(λ) is a wildcard character substituted for the sub-modules AD#_(α)˜AD#_(m), wherein AD#_(m) excludes the threshold switch group LJKGZ_(m); U_(λy) is an input voltage at stage λ; R_(λ8)˜R_(λ0) is a voltage-dividing resistor chain at stage λ; V_(λ7)˜V_(λ0) are potential reference points at stage λ; C_(λ7)˜C_(λ1) are comparators at stage λ; I*_(λ7)˜I*_(λ1) are comparison values at stage λ; I_(λ8) is constantly zero and I_(λ0) is constantly 1; D_(λ2)˜D_(λ0) are digital output values at stage λ; V_(p) is the anode of the power source; S_(λ7)˜S_(λ0) are switching points of the threshold switches at stage λ; a solid frame LJKGZ_(λ) comprising S_(λ7)˜S_(λ0) and the control characters I_(λ8)˜I_(λ0) is the threshold switch group; I_(λ8)˜I_(λ0) are the control characters; I*_(λg) and I_(λg), referring to the same control character, are connected through wires, and so are I_(g) and I*_(g); S_(λ) is the switch main line at stage λ; V′_(λg) is a stage-potential-to-be at stage λ; V_(λG) (unshown) is a stage-potential at stage λ; V_(λ0) is a bottom potential; Σ′_(λ) is an elevation summator at stage λ; Σ_(λ) is a residue summator at stage λ; U_(λZ) is a to-be-compared voltage at stage λ; CB_(λ) is a sampler/holder at stage λ; U*_(λy) is a sampled/held voltage; U_(λx) is a residue voltage at stage λ; FD_(λ) is a residue voltage amplifier at stage λ; U_(μy) is an amplified value of the residue voltage U_(λx), and U_(μy) is also an input voltage of the next sub-module, AD#_(μ); a hollow triangle is a voltage follower.

FIG. 2.2 is a block diagram of the front-end circuit QZDL according to Embodiment 2.2 of the present invention, wherein original input alternating signal-u_(αy); sampler/holer-CB; alternating sampling/holding signal-u_(g); positive-negative discriminator-ZFP_(x); positive input voltage-U_(g); polarity register-D_(X); analog logarithmic compression law module-Log; input voltage at stage α-U_(αy).

FIG. 2.3 is a schematic diagram of the positive-negative discriminator according to Embodiment 2.3 of the present invention, wherein a dashed frame ZFP represents the positive-negative discriminator; u_(g), U_(g) and D_(X) are as illustrated above; operational amplifier YF comprises a positive-negative comparator YF_(A) and an inverter YF_(B); inverter input resistor and feedback resistor-R_(C5) and R_(C6); inverting switch-S_(X).

FIG. 3.1A is an enlargement view of part A of FIG. 3.1; FIG. 3.1B is an enlargement view of part B of FIG. 3.1.

FIG. 3.1 is a schematic diagram of m stages*3-bit equal resistance type logarithmic DAC according to Embodiment 3.1 of the present invention, wherein V_(λG), V′_(λG), R_(λ8)˜R_(λ0), V_(λ7)˜V_(λ0), I_(λ8)˜I_(λ0), S_(λ), CB_(λ), GS, LJKGZ_(λ), multi-channel switch DLKG_(λ) and stage-potential switch JDWKG_(λ) are all as illustrated above; further, logarithmic sub-DAC at stage λ-DA#_(λ), decoder at stage α-solid frame JM_(α), input terminals of JM_(α)−d_(α2)˜d_(α0). Herein the control characters I_(α7)˜I_(α1) obtained after decoding determine a stage-potential strobe point S_(αG); JM_(α)+LJKGZ_(α)=DLKG_(α); and thus d_(α2)˜d_(α0) are not only the input terminals of JM_(α), but also control terminals of the multi-channel switch DLKG_(α); attenuator at stage λ−Ψ_(λ); analog output signal voltage at stage λ, or output voltage for short-V_(λΨ); overall summator −Σ_(Ψ); overall output analog voltage V_(Ψ).

FIG. 3.2.1 is a sketch view of the triangle GS, the voltage follower, according to Embodiment 3.1 of the present invention, wherein an output voltage and an input voltage are both U_(X2) and thus equal, while a loading capacity is enhanced. The triangle represents the voltage follower throughout all of the drawings, with or without GS.

FIG. 3.2.2 is a sketch view of a proportional attenuator Ψ_(X) according to Embodiment 3.1 of the present invention, wherein Ψ in upper case is a symbol of the proportional attenuator; subscript X is a wildcard character; ψ_(X) in lower case (unshown) is an attenuation proportion; input signal U_(X1), output signal U_(X2) and the attenuation proportion ψ_(X) satisfy an equation of: U_(X2)=U_(X1)/ψ_(X).

FIG. 3.2.3 is a structural diagram of the proportional attenuator Ψ_(X) according to Embodiment 3.1 of the present invention, wherein an integrated op-amp GS, namely the voltage follower in FIG. 3.2.1, R_(X1) and R_(X2) form a voltage-dividing circuit; because a non-inverting terminal of the voltage follower GS is an input terminal, which leads to a virtual opening and zero current, equal currents run through R_(X1) and R_(X2), and thus U_(X2)=U_(X1)*R_(X2)/(R_(X1)+R_(X2)); let ψ_(X)=(R_(X1)+R_(X2))/R_(X2), U_(X2)=U_(X1)/ψ_(X).

FIG. 4A is an enlargement view of part A of FIG. 4; FIG. 4B is an enlargement view of part B of FIG. 4.

FIG. 4 is a schematic diagram of a two-stage logarithmic chain ADC according to Embodiment 4 of the present invention. Because of logarithmic relations between the resistor chain and a reference potential chain, the ADC is called the logarithmic chain ADC represented by LAD##; the logarithmic chain ADC comprises two sub-stages, LAD#_(α) and LAD#_(β); LAD#_(α) is a first-stage logarithmic chain sub-ADC, and LAD#_(β) is a second-stage logarithmic chain sub-ADC; second-stage elements, namely stage β elements, are marked with single quotes ’, while first-stage elements, namely stage α elements, are without the single quotes ’.

In FIG. 4, LAD#_(α) comprises LBXQ_(α), JDWKG and QHFD, wherein LBXQ_(α), a first-stage logarithmic chain parallelizer, comprises a first-stage logarithmic resistor chain R_(Q)˜R₁ and R_(θ), first-stage logarithmic reference potential points V_(Q−1)˜V_(θ), first-stage comparators C_(Q−1)˜C₁, first-stage comparison values I_(Q−1)˜I₁, a first-stage encoder BM and first-stage logarithmic digital output signals D_(q−1)˜D₀; QHFD, a summing and amplifying operational circuit, comprises first-stage summators Σ_(Q−1)˜Σ₀, difference voltages U_(X(Q−1))˜U_(X0), amplifiers F_(Q−1)˜F₀, operational voltages U_(y(Q−1))˜U_(y0) and an operational stage voltage U_(yG); and JDWKG, a stage-potential switch, comprises switching points S_((Q−1))˜S₀, control terminals d_(q−1)˜d₀ of a multi-channel switch, first-stage control characters I_(Q−1)˜I₁, I_(Q) constantly zero, I₀ constantly 1, a switch main line S_(α) and a strobe point voltage drop V_(r).

In FIG. 4, a main component of LAD#_(β) is a second-stage logarithmic chain parallelizer LBXQ_(β); LBXQ_(β) comprises a second-stage logarithmic resistor chain R′_(T)˜R′₁, wherein second-stage logarithmic reference potential points V′_(T−1)˜V′₀ are respectively connected to inverting terminals of second-stage comparators C′_(T−1)˜C′₁; a second-stage to-be-compared voltage U_(βZ) is connected to a non-inverting terminal of each second-stage comparator; and then second-stage comparison values I′_(T−1)˜I′₁ are obtained and encoded by a second-stage encoder into second-stage digital output signals D′_(t−1)˜D′₀; LBXQ_(β) further comprises a sampler/holder CB_(β), an operational stage voltage-to-be U′_(yG), an operational stage voltage U_(yG) and the second-stage to-be-compared voltage U_(βZ).

FIG. 5A is an enlargement view of part A of FIG. 5; FIG. 5B is an enlargement view of part B of FIG. 5.

FIG. 5 is a schematic diagram of a two-stage logarithmic chain DAC according to Embodiment 5 of the present invention. Because of logarithmic relations between the resistor chain and the reference potential chain, the DAC is called the logarithmic chain DAC represented by LDA##; the logarithmic chain DAC comprises two sub-stages, LDA#_(α) and LDA#_(β); LDA#_(α) is a first-stage logarithmic chain sub-DAC, and LDA#_(β) is a second-stage logarithmic chain sub-DAC; second-stage elements, namely stage β elements, are marked with single quotes ’, while first-stage elements, namely stage α elements, are without the single quotes ’.

In FIG. 5, LDA#_(α) comprises DZL_(α), SJQH, JDWKG and Σ_(AU), wherein DZL_(α), a first-stage logarithmic resistor chain, comprises a first-stage logarithmic resistor chain R_(Q)˜R₁ and R_(θ), and first-stage logarithmic reference potential points V_(Q−1)˜V_(θ); SJQH, an attenuating and summing module, comprises attenuators Ψ_(Q−1)˜Ψ₀, second-stage stage-potential attenuated value V_(Ψ(Q−1))˜V_(Ψ0), summators Σ_(Q−1)˜Σ₀, reference potential sum values V_(Σ(Q−1))˜V_(Σ0) and a follower GS; JDWKG, a first-stage stage-potential switch, comprise first-stage control characters I_(Q−1)˜I₂, I_(Q) constantly zero, I₀ constantly 1, first-stage switching points S_((Q−1))˜S₀, and control terminals d_(q−1)˜d₀ of a first-stage multi-channel switch; and Σ_(AU), a collecting module, comprises a collector Σ_(αU), stage-potential sum values U_(Σ(Q−1))˜U_(Σ0) and an analog voltage output value U_(αβ).

In FIG. 5, LDA#_(β) comprises DZL_(β), JDWKG′ and Σ_(βU), wherein DZL_(β), a second-stage logarithmic resistor chain, comprises a second-stage logarithmic resistor chain R′_(T)˜R′₁, and second-stage logarithmic reference potential points V′_(T−1)˜V′₀; JDWKG′, a second-stage stage-potential switch, comprise second-stage control characters I′_(T−1))˜I′₁, I′_(T) constantly zero, I′₀ constantly 1, second-stage switching points S′_((T−1))˜S′₀, and control terminals d′_(t−1)˜d′₀ of a second-stage multi-channel switch.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Numbers of the preferred embodiments correspond to the view numbers of the drawings.

Embodiment 1.1 Threshold Switch

Each threshold switch is controlled under two control characters. The threshold switch at step g stage λ S_(λg) is controlled under the control characters I_(λ(g+1)) and I_(λg) based on control relations showed in Table 3. When I_(λg)=0 or I_(λ(g+1))=1, the threshold switch S_(λg) cuts off signal; only when I_(λg)=1 and I_(λ(g+1))=0, the threshold switch S_(λg) transmits signal. The threshold switch comprises a lossy switch and a lossless switch provided by the present invention.

Embodiment 1.1.1 Follower Switch

The lossless switch comprises a follower switch which functions as a signal switch for transmitting or blocking the signal; a voltage follower switch comprises two modules, a module of a follower and a module of a power source switch; the power source switch is an electronic device provided on a power source loop of the follower, and controls connection and disconnection of the power source loop of the follower through the control characters.

The follower is at a state of following voltage when the operational power source is connected, or powering on. Herein the signal is inputted through a non-inverting terminal of the follower; a voltage of an output terminal is accurately equal to a voltage of the non-inverting terminal, in such a manner that the signal is transmitted from the input terminal into the output terminal, which is called signal-on, with a extremely small voltage drop (smaller than 10⁻⁸V). Technically speaking, such a small voltage drop can be seen as zero voltage drop or zero on-resistance, which is similar to an ideal short circuit connection. When the operational power is cut off, or powering off, the output terminal and the non-inverting terminal of the follower are at a state of blocking signal which is also called signal-off. Herein the output terminal and the non-inverting terminal have extremely large resistances (as large as 10⁹Ω). Technically speaking, such a large resistance can be seen as infinitely large, which is similar to an ideal cutting off.

The follower switch transmits the signal when powering on and blocks the signal when powering off, so the follower switch is capable of controlling the connection and disconnection of the power source loop through the control characters, so as to further control connection and disconnection of a signal loop of the follower. Logic relations about the connection and disconnection of the follower switch formed by the control characters is optional, such as normally open, normally close and threshold switching. In the embodiment of the present invention, the follower switch is embodied as a threshold switch having the logic relations of Table 3. The threshold switch S_(λg) is embodied into various circuit structures; following S_(λg1), S_(λg2) and S_(λg3) are only exemplary.

Embodiment 1.2.1 Lossless Switch S_(λg1)

The follower A_(λg) of the lossless switch S_(λg1) comprises an integrated op-amp whose inverting terminal and output terminal are in a short connection. Transistors VT1, VT3, VT0 and VT2 are provided on a power supply loop of A_(λg). Only when I_(λg)=1 and I_(λ(g+1))=0, A_(λg) is powered on and thus signal-on, wherein A_(λg) is powered on only when I_(λg)=1 indicating that VT1 and VT3 are in a saturation conducting, and I_(λ(g+1))=0 indicating that VT0 and VT2 are in a saturation conducting. Otherwise, when I_(λ(g=1))=0 or I_(λ(g+1))=1, A_(λg) is powered off, wherein once I_(λg)=0 VT1 and VT3 are cutting off, and once I_(λ(g+1))=1 VT0 and VT2 are cutting off too; herein A_(λg) has no amplification effects and is signal-off because of an extremely large input resistance of the non-inverting terminal.

For simplification, one of VT0 and VT2 is arbitrarily in short circuit; one of VT1 and VT3 is arbitrarily in short circuit.

Embodiment 1.2.2 Lossless Switch S_(λg2)

Transistors VT4, VT5, VT6, VT7, VT8 and VT9 are provided a power supply loop of the voltage follower A_(λg) of the lossless switch S_(λg2). Only when I_(λg)=1 and I_(λ(g+1))=0, A_(λg) is powered on and thus signal-on, wherein when I_(λg)=1 VT6 and VT9 are in a saturation conducting, and when I_(λ(g+1))=0 VT5 and VT8 are cutting off, so that VT4 and VT7 are in a saturation conducting. Otherwise, when I_(λg)=0 or I_(λ(g+1))=1, A_(λg) is powered off and thus signal-off, wherein once I_(λg)=0 VT6 and VT9 are cutting off, and once I_(λ(g+1))=1 VT5 and VT8 are in a saturation conducting, which leads to low potentials of collector terminals V_(5C) and V_(8C) and further leads to cutoff of VT4 and VT7.

For simplification, one of VT6 and VT9 is arbitrarily in short circuit; one of VT4 and VT7 is arbitrarily in short circuit.

Embodiment 1.2.3 Lossless Switch S_(λg3) in Broad Sense

The power source switch which controls powering on and powering off A_(λg) has various embodiments. In the broad sense, KS1 and KS3 are power source switches conducting at high potential; KS0 and KS2 are power source switches conducting at low potential. Only when I_(λg)=1 and I_(λ(g+1))=0, KS1 and KS3 are conducting, and, KS0 and KS2 are also conducting, in such manner that A_(λg) is powered on and thus signal-on. Otherwise, when I_(λg)=0 or I_(λ(g+1))=1, KS1 and KS3 are cutting off, or, KS0 and KS2 are cutting off, in such a manner that A_(λg) is powered off and thus signal-off.

Embodiment 1.2.4-q-Bit Multi-Channel Switch

The q-bit multi-channel switch comprises threshold switches at steps 0˜(Q−1) stage λ S_(λ0)˜S_(λ(Q−1)), wherein the threshold switches are within a frame of a threshold switch group at stage λ, represented by LJKGZ_(λ); potentials of input terminals at steps 0˜(Q−1) stage λ V_(λ0)˜V_(λ(Q−1)); control characters at steps 0˜(Q−1) stage λ I_(λ0)˜I_(λQ); control terminals of the multi-channel switch at stage λ d_(λ0)˜d_(λ(q−1)); and a decoder JM_(λ) for decoding digital signals at the control terminals into the control characters at steps 0˜(Q−1) stage λ I_(λ0)˜L_(λQ) and then obtaining a strobe terminal among the potentials of the input terminals at steps 0˜(Q−1) V_(λ0)˜V_(λ(Q−1)).

Embodiment 2.1-m Stages*q-Bit Equal Resistance Logarithmic ADC

In order to simplify the illustration of the present invention, all sub-stages in Embodiment 2.1 and Embodiment 3.1 are q-bit, although theoretically each sub-stage can have different bit numbers. After being processed by a front-end circuit QZDL, an original input alternating signal u_(αy) becomes an input voltage at stage α U_(αy); an input voltage at stage λ, U_(λy) ranges between 0˜V_(p); the sub-ADC at stage λ, AD#_(λ) processes the input voltage at stage λ, U_(λy) with an AD conversion through following five modules and processes thereof.

-   -   (1) Stage-Potential V_(λG) Generating Module

Let Q=2^(q), a voltage-dividing resistor chain of a parallelizer at stage λ R_(λ(Q−1))˜R_(λ0) (R_(λ0)=R′_(λ0)+R_(λS)) form potential reference points at stage λ V_(λ(Q−1))˜V_(λ0), wherein V_(λ0) is a bottom potential. The reference points V_(λ(Q−1))˜V_(λ1) are correspondently connected to inverting terminals of comparators C_(λ(Q−1))˜C_(λ1) in the parallelizer. The input voltage at stage λ U_(λy) becomes a temporary stable voltage U*_(λy) through sampling and holding; then summing the bottom potential V_(λ0) and the temporarily stable voltage U*_(λy) forms a to-be-compared voltage U_(λZ); the to-be-compared voltage U_(λZ) is connected to non-inverting terminals of the comparators C_(λ(Q−1))˜C_(λ1), for being compared with the potential reference points V_(λ(Q−1))˜V_(λ0). Because V_(λQ)>U_(λZ)>V_(λ0), there always exists a threshold point V_(λG) which is called a stage-potential within (V_(λQ)˜V_(λ0)). Through V_(λ(G+1))>U_(λZ)>V_(λG), a threshold point G of comparison values at stage λI_(λ(Q−1))˜I_(λ1) is determined, satisfying requirements of I_(λ(Q−1))˜I_(λ(G+1))=0 and I_(λG)˜I_(λ1)=1; let I_(λQ) constantly 0 and I_(λ0) constantly 1, the comparison values I_(λ(Q−1))˜I_(λ0) are encoded by an encoder BM_(λ), and then digital output values D_(λ(q−1))˜D_(λ0) of the stage-potential V_(λG) are obtained. Herein, with the stage-potential V_(λG) as a bridge, the to-be-compared U_(λZ) is converted into the stage-potential V_(λG) and further into the digital signals D_(λ(q−1))˜D_(λ0).

(2) Switch Error Reducing Module

The switch error reducing module reduces switch errors with following two manners. The first manner is applying identical elevation to the potential of the reference points and the input voltage. Because the conventional analog signal switch (abbreviated as switch) naturally has voltage drop, the reference point potential V_(λ0) correspondent to S_(λ0) needs to be high enough to close S_(λ0), and thus the divided voltage V_(λ0) obtained through R_(λ0) is capable of ensuring closing S_(λ0). Further, because the potentials of the reference points are all elevated by V_(λ0), the temporarily stable voltage U*_(λy) also needs an elevation of V_(λ0) for an offset, which is accomplished by extracting V_(λ0) with a follower, sending the extracted V_(λ0) into an elevation summator Σ′_(λ) and elevating the input voltage U*_(λy) into the to-be-compared voltage U_(λZ). Speaking from an aspect of comparing potential, elevating both the potentials of the reference points and the input voltage is equivalent to elevating neither one. After the stage-potential V_(λG) is extracted, the strobe point S_(λG) decreases by the switch voltage drop V_(λS) into the stage-potential-to-be V′_(λG). Generally, each switch has a different voltage drop; in the present invention, difference among the voltage drops are ignored, and the voltage drops are uniformly represented by V_(λS). Let R_(λ0)=R′_(λ0)+R_(λS), and let the voltage drop of R_(λS) exactly equal to V_(λS), V_(λS) is extracted by the follower and then sent into a residue summator Σ_(λ) for calculation, so as to obtain a residue voltage U_(λX)=U_(λZ)−V′_(λG)−V_(λS). The second manner is using the lossless switch. The lossless switch has zero voltage drop, so the stage-potential V_(λG) extracted via the strobe point S_(λG) gets held. As showed in FIG. 2.1, let R′_(λ0)=0 and R_(λS)=0, then V_(λ0)=0 and V_(λS)=0, which means that R′_(λ0) and R_(λS) can be eliminated, and that the follower and the elevation summator Σ′_(λ) correspondent to V_(λ0) and V_(λS) also can be eliminated; herein U_(λZ)=U*_(λy), and V′_(λG)=V_(λG).

(3) Stage-Potential V_(λG) Extracting Module

All sub-stages in AD## needs a module to extract out the stage-potential V_(λG) for a preparation of the conversion at next sub-stage, except the final sub-stage. The stage-potential is extracted for the conversion at next sub-stage. Given that a conversion bit number of each sub-stage is q, Q=2^(q); the voltage V_(p) is divided by the resistor chain into Q equal voltages; each equal divided voltage ΔV is a fixed value ΔV=V_(p)/Q. The stage-potential V_(λG) is lower than the to-be-compared voltage U_(λZ), but is the closest reference potential to the to-be-compared voltage U_(λZ); and thus, within a measurement accuracy at stage λ, V_(λG)=U_(λZ). The stage-potential switch, a module for finishing the extraction of the stage-potential V_(λG), comprises the threshold switch group LJKGZ_(λ), and the multi-channel switch DLKG_(λ), wherein the reference potential points V_(λ(Q−1))˜V_(λ0) are arithmetically connected to the switch points S_(λ(Q−1))˜S_(λ0) one by one. A solid frame LJKGZ_(λ), in AD#_(λ) represents the threshold switch group, wherein the strobe point S_(λG) is determined through the strobe control of the threshold switch group as illustrated above. The strobe point S_(λG) corresponds to the stage-potential V_(λG), and sends the stage-potential V_(λG) into the switch main line S_(λ).

(4) Inter-Stage Operation Module

The inter-stage operation module comprises a sampler/holder CB_(λ), the residue summator Σ_(λ) and a residue amplifier FD_(λ). The input voltage at stage λ U_(λy) becomes the stable U*_(λy) through the sampler/holder CB_(λ); the input voltage of each sub-stage maintains independent and stable within a sampling cycle through the inter-stage sampler/holder CB_(λ), in such a manner that m sub-stages are capable of parallel operating for forming an pipeline-typed conversion. The residue summator Σ_(λ) generates the residue voltage U_(λX)=U_(λZ)−V′_(λG)−V_(λS). The residue voltage U_(λx) is within 0˜ΔV; the residue amplifier FD_(λ) amplifies the residue voltage signal Q times, so as to generate U_((λ+1)y)=U_(μy)=Q*U_(λx). As a result, a range of U_(λy) expands into the full scale of 0˜V_(p), and U_(μy) becomes the input voltage at stage λ+1 (stage μ). The input voltage at stage μ U_(μy) enters AD#_(μ) at stage μ for the measurement and conversion at a higher accuracy.

(5) Logarithmic Conversion Module and Process Thereof

The logarithmic conversion module comprises an analog conversion and a digital conversion. The digital conversion module is based on converting the overall input voltage U_(αy) into high-bit digital signals having equal quantization distances, and converting the high-bit digital signals into low-bit digital signals having logarithmic quantization distances through a logarithm table. The analog conversion module is based on converting a linear input voltage into the logarithmic input voltage through an analog logarithm converter before inputting at stage α, while in fact ADC is for converting the logarithmic input voltage into the digital signals having the logarithmic quantization distances.

Embodiment 2.2 Front-End Circuit QZDL

The front-end circuit QZDL works in following principles. When a sampling execution signal arrives, the sampler/holder CB processes the original input alternating signal u_(αy) with sampling and holding, so as to generate an alternating sampling/holder signal u_(g) which maintains stable within the sampling cycle. A positive-negative discriminator ZFP_(X) of the front-end circuit QZDL judges and processes a polarity of u_(g); when u_(g)>0, let a polarity register D_(X)=0, then a discrimination output signal of ZFP_(X) U_(g)=u_(g); when u_(g)<0, let D_(X)=1, U_(g)=−u_(g). As a result, U_(g) only has the positive polarity because U_(g)=|u_(g)| and thus is called a positive input voltage U_(g). An analog logarithmic compression law module Log is optional; the Log module is necessary for the analog LOG compression law. Herein, one skilled in the art is familiar with the arts of the Log module, so the illustration of the Log module is omitted; the logarithmic compression referred in the present invention comprises A-law and μ-law which are approximations to the logarithmic compression law. When QZDL further comprises the Log module, the input voltage at stage α U_(αy) is equal to the logarithmic compression law of U_(g), and the evenly spaced AD conversion generates the digital signals of the logarithmic compression law. When QZDL excludes the Log module, U_(αy)=U_(g), and the AD conversion is linear.

Embodiment 2.3 Signal Positive-Negative Discriminator

The signal positive-negative discriminator works in following principles. When u_(g) is positive, YF_(A) outputs a low potential, and D_(X)=0; S_(X) is toggled upwardly for directly outputting u_(g) into U_(g); R_(C5)=R_(C6), so YF_(B) is amplified −1 times. When u_(g) is negative, YF_(A) outputs a high potential, and D_(X)=1; S_(X) is toggled downwardly, in such a manner that an inverter phase of u_(g) is outputted into U_(g) through YF_(B).

Embodiment 3.1-m Stages*q-Bit Equal Resistance Logarithmic DAC

N-bit digital signals are allocated as m stages*q-bit: (D_((N−1)), . . . , D₀)=(D_(α(q−1)), . . . , D_(α0)), (D_(β(q−1)), . . . , D_(β0)), . . . , (D_(m(q−1)), . . . , D_(m0)). D are sent into the control terminals of the correspondent stage-potential switches: (d_(α(q−1)), . . . , d_(α0)), (d_(β(q−1)), . . . , d_(β0)), . . . , (d_(m(q−1)), . . . , d_(m0)).

The sub-DAC_(λ) at stage λ processes the digital signals at stage λ (D_(λ(q−1)), . . . , D_(λ0)) with a DA conversion through following four modules and processes thereof

(1) Stage-Potential V_(λG) Generating Module

Q=2^(q); a voltage-dividing resistor chain R_(λQ)˜R_(λ0) of a parallelizer at stage λ forms potential reference points V_(λ(Q−1))˜V_(λ0) at stage λ. After the stage-potential V_(λG) generating module receives the digital signals (D_(λ(q−1)), . . . , D_(λ0)), the reference potential point V_(λG) correspondent to the digital signals becomes the stage-potential; V_(λ0) is a bottom potential.

(2) Switch Error Reducing Module, Identical to the Switch Error Reducing Module of Embodiment 2.1

(3) Stage-Potential V_(λG) Extracting Module

The stage-potential V_(λG) of each stage needs to be extracted out for calculating an output voltage V_(λΨ) of each stage. The stage-potential V_(λG) extracting module and a process thereof in Embodiment 3.1 are identical to the stage-potential V_(λG) extracting module and process in Embodiment 2.1.

(4) Inter-Stage Operational Module

The stage-potential V_(λG), the output voltage V_(λΨ) and an attenuation coefficient Ψ_(λ) have a relation of: V_(λΨ)=V_(λG)/Ψ_(λ), wherein Q=2^(q); Ψ_(λ)=Q^((λ−1)), namely the attenuation coefficient of an attenuator Ψ_(λ) at stage λ Ψ_(λ)=Q^((λ−1)). λ is a wildcard character substituted for α, β, γ, . . . , m; α, β, γ, . . . represented with numbers are α=1, β=2, γ=3, . . . ; and thus, λ represents the stage. For example, stage γ is stage 3, λ=3, then Ψ_(λ)=Q². A summation of V_(λΨ) of all stages is executed by an overall summator Σ_(Ψ), so as to generate an overall output analog voltage V_(Ψ). After the attenuation and the summation, the bottom potential of each stage becomes equal to a constant V_(RS): V_(RS)=V_(α0)/Ψ_(α)+V_(β0)/Ψ_(β)+ . . . +V_(m0)/Ψ_(m)=V_(α0)/(Q^(m−α))+V_(β0)/(Q^(m−β))+ . . . +V_(m0)/(Q^(m−m)). A waveform of the overall output analog voltage V_(Ψ) is only elevated by V_(RS), without being transformed; the waveform of the overall output analog voltage V_(Ψ) is obtained by subtracting V_(RS) in the overall summator Σ_(Ψ).

(5) Logarithmic Conversion Module

The logarithmic conversion module comprises an analog conversion module and a digital conversion module. The digital conversion module is based on, after receiving low-bit digital signals having logarithmic quantization distances, converting the digital signals into high-bit digital signals having equal quantization distances through an anti-logarithm table, and then converting the high-bit digital signals into analog signals by a high-bit DAC having equal quantization distances. The analog conversion module is based on, after accomplishing the DA conversion by the DAC, converting the logarithmic analog signals into a linear output voltage by an analog anti-logarithmic converter.

Embodiment 4 Two-Stage Logarithmic Chain ADC

The logarithmic chain ADC comprises two sub-stages, LAD#_(α) and LAD#_(β). LAD#_(α) is a first-stage logarithmic chain sub-ADC, and LAD#_(β) is a second-stage logarithmic chain sub-ADC. According to the Embodiment 4 of the present invention, the two-stage logarithmic chain ADC comprises the lossless switch.

The first-stage LAD#_(α) executes a q-bit conversion. A logarithm law resistor chain R_(Q)˜R₁ and R_(θ) divides a voltage 0˜V_(P) into Q+1 segments, forming Q+2 potential points. Except 0 and V_(P), V_(Q−1)˜V_(θ) are reference potential points, or quantized points, which have Q=2^(q) steps. The reference potential chain V_(Q−1)˜V_(θ) are set as the logarithm law; V_(Q−1)˜V₁ are connected to inverting terminals of correspondent first-stage comparators C_(Q−1)˜C₁, and a first-stage to-be-compared voltage U_(αZ) is connected to non-inverting terminals of each first-stage comparator, so as to generate first-stage comparison values I_(Q−1)˜I₁; Through encoding the first-stage comparison values by a first-stage encoder BM, first-stage logarithmic digital output signals D_(q−1)˜D₀ are generated. A stage-potential V_(G) of the to-be-compared voltage U_(αZ) is obtained by controlling a stage-potential switch JDWKG via the first-stage comparison values I_(Q−1)˜I₁ or the digital output signals D_(q−1)˜D₀, namely obtaining a rough result of U_(αZ) about a detection that to which segments of the first-stage-potential chains the to-be-compared voltage U_(αZ) belongs. The to-be-compared voltage U_(αZ) is connected to first-stage summators Σ_(Q−1)˜Σ₀ to be minuends, and the reference potential points V_(Q−1)˜V_(θ) are correspondently connected to Σ_(Q−1)˜Σ₀ to be subtrahends, so as to generated difference voltages U_(X(Q−1))˜U_(X0). Then, the difference voltages U_(X(Q−1))˜U_(X0) are sent into first-stage amplifiers F_(Q−1)˜F₀ to generate operational voltages U_(y(Q−1))˜U_(y0). The difference voltage correspondent to the stage-potential V_(G) is called a residue voltage U_(XG) which is unshown because of a random position of U_(XG). The operational voltage correspondent to the stage-potential V_(G) is called an operational stage-potential U_(yG). The summators acquires that the residue voltage U_(XG)=U_(αZ)−V_(G) and that U_(XG) ranges within (0˜ΔV_(G)), wherein ΔV_(G) is a quantization distance of the stage-potential; ΔV_(G)=(V_((G+1))−V_(G)). Let an amplification coefficient of the amplifier F_(G) be V_(p)/ΔV_(G), the amplifier F_(G) generates the operational stage voltage U_(yG)=U_(XG)*V_(p)/ΔV_(G). After U_(XG) is amplified into U_(yG), the voltage range expands into a full scale of 0˜V_(p). The stage-potential switch extracts out the operational stage voltage U_(yG) and sends the extracted U_(yG) into a switch main line S_(α) towards the next stage. U_(yG) becomes the to-be-compared voltage at the next stage U_(βZ) after being sampled and held by a sampler/holder CB_(β), before an accurate measurement at the next stage. The input voltages of the two sub-stages maintain independent and stable within a sampling cycle due to the inter-stage sampler/holder CB_(β), in such a manner that the two sub-stages are capable of parallel operating and form a pipeline-type conversion.

The second-stage LAD#_(β) mainly comprises a second-stage logarithmic chain parallelizer LBXQ_(β), wherein second-stage logarithmic resistor chain R′_(T)˜R′₁ form potential points V_(P) and V′_(T−1)˜V′₀. Except V_(p), V′_(T−1)˜V′₀ are second-stage logarithmic reference potential points. V′_(T−1)˜V′₁ are connected to correspondent inverting terminals of second-stage comparators C′_(T−1)˜C′₁, and the second-stage to-be-compared voltage U_(βZ) is connected to a non-inverting terminal of each second-stage comparator, so as to generate second-stage comparison values I′_(T−1)˜I′₁. Then the second-stage comparison values I′_(T−1)˜I′₁ are encoded by a second-stage encoder BM′ to generate second-stage logarithm law digital signals D′_(t−1)˜D′₀. The two sub-stages, LAD#_(α) and LAD#_(β), together accomplish the digital signals conversion of the q+t bits logarithm law, wherein D_(q−1)˜D₀ are high bit and D′_(t−1)˜D′₀ are low bit.

In order to increase an SNR and broaden a signal dynamic range, the logarithmic resistor chain is preferred. The resistor chains of the two sub-stages, LAD#_(α) and LAD#_(β) are set according to the logarithm law as follows.

The first-stage resistor chain is logarithmically provided as follows. The resistor chain of LAD#_(α) has a constant resistance, so a chain current I_(α) is also constant. Let a base potential V_(θ) be equal to a minimum effective detection value of a sensor, and let a base resistance R_(θ)=V_(θ)/I_(α) and R_(A)/R_(θ)=η−1, wherein R_(A) is a virtual start resistance, the first-stage chain resistances successively increase by a large ratio of η^(T) from R_(A), which forms a large ratio resistor chain: R₁=R_(A)*η^(T), R₂=R_(A)*η²*^(T), . . . , R_(Q−3)=R_(A)*η^((Q−3))*^(T), R_(Q−2)=R_(A)*η^((Q−2))*^(T), R_(Q−1)=R_(A)*η^((Q−1))*^(T). The large ratio resistor chain R_(θ)˜R_(Q) forms a large ratio potential chain (V_(j+1)/V_(j)=η^(T)): ground, V_(θ), V₁=V_(θ)*η^(T), V₂=V_(θ)*η²*^(T), V₃=V_(θ)*η³*^(T), . . . , V_(Q−2)=V_(θ)*η^((Q−2))*^(T), V_(Q−1)=V_(θ)*η^((Q−1))*^(T), V_(Q)=V_(θ)*η^(Q)*^(T)=V_(p). Except V_(Q)=V_(P), Q reference potential points, also called quantized points, are: V_(θ), V₁, . . . , V_(Q−1). Because a region below V_(θ) is an invalid detection region of the sensor, V_(θ) is the quantized point of the region of (V₁˜V_(θ)˜0) which is marked as (V₁˜V_(θ)˜0)→V_(θ); quantization intervals of the other quantized points are: (V₂˜V₁]→V₁, (V₃˜V₂]→V₂, . . . , (V_(Q−1)˜V_(Q−2)]→V_(Q−2), (V_(Q)˜V_(Q−1)]→V_(Q−1). Since the first-stage quantized points are rough because of the large ratio η^(T), it is necessary to insert T second-stage fine quantized points having a small ratio of η therebetween.

The second-stage resistor chain is logarithmically provided as follows. The resistor chain of LAD#_(β) comprises T=2^(t) resistors, R′₁˜R′_(T). As illustrated above of the first sub-stage, the residue voltage U_(XG)=U_(αZ)−V_(G) ranges within (0˜ΔV_(G)); ΔV_(G)=(V_((G+1))−V_(G)); V_(G)=V_(θ)*η^(G)*^(T), V_((G+1))=V_(θ)*η^((G+1))*^(T), wherein ΔV_(G) is the quantization step of the first-stage stage-potential V_(G). Theoretically, T fine quantized points of the second sub-stage need to be inserted into V_(G)˜V_((G+1)); the fine quantized points of V_(G)˜V_((G+1)) comprise V″₀=V_(G)=V_(θ)*η^(G)*^(T), V″₁=V_(G)*η¹, V″₂=V_(G)*η², V″₃=V_(G)*η³, . . . , V″_(T−2)=V_(G)*η^(T−2), V″_(T−1)=V_(G)*η^(T−1), wherein the fine quantized points increase geometrically by a ratio of η. V″_(T)=V_(G)*η^(T)=V_(G+1) is the quantized point at first-stage next step, and thus excluded from the inserted points. Thus once the second-stage resistor chain has the geometrical relation of η and is multiplied by a coefficient, the second-stage resistor chain is capable of accomplishing the logarithmic conversion of the residue voltage. Actually, the second-stage conversion is extracting out the first-stage residue voltage U_(XG), rather than inserting the fine quantized points into V_(G)˜V_((G+1)). U_(XG) ranges within (0˜ΔV_(G)); the first-stage residue voltage U_(XG) expands into the first-stage operational stage voltage U_(yG) after being amplified by the correspondent amplifier F_(G). Let the amplification coefficient of the amplifier F_(G) be V_(p)/ΔV_(G), U_(yG)=U_(XG)*V_(p)/ΔV_(G), and the range of (0˜ΔV_(G)) is expanded into the full scale of 0˜V_(p). The operational stage voltage U_(yG) becomes the second-stage to-be-compared voltage U_(βZ) after being sampled and held by the sampler/holder CB_(β). It is a key of the second-stage resistor chain to establish the logarithm law quantized points. In the second-stage resistor chain, R_(B) is an arbitrary virtual resistance, values of T chain resistors increase geometrically by the ratio of η:R′₁, R′_(B)*η¹, R′₂−R_(B)*η², R′₃=R_(B)*η³, . . . , R′_(T−2)=R_(B)*η^(T−2), R′_(T−1)=R_(B)*η^(T−1), R′_(T)=R_(B)*η^(T), and then naturally T quantized points whose potentials geometrically increase by the ratio of η are formed: 0, V′₁=V_(B)*η¹, V′₂=V_(B)*η², V′₃=V_(B)*η³, . . . , V′_(T−2)=V_(B)*η^((T−2)), V′_(T−1)=V_(B)*η^((T−1)), as well as the quantization intervals thereof: (V′₁˜0]→0, (V′₂˜V′₁]→V′₁, (V′₃˜V′₂]→V′₂, . . . , (V′_(T−1)˜V′_(T−2)]→V′_(T−2), (V′_(T)˜V′_(T−1)]→V′_(T−1). V′_(T)=V_(P) is excluded from the second-stage quantized points.

Herein, the two-stage logarithmic chain ADC converts the analog signals into the logarithmic digital signals. As showed in FIG. 1.3, a curve 3 represents the constant SNR of the digital signals. Further, if the base resistance R_(θ) is adjusted into an adjustment resistance R*_(θ), wherein R*_(θ)=R_(θ)˜R_(θ)/15, let R*_(θ) be the minimal effective signal of the sensor, by reducing the adjustment resistance R*_(θ), showed as a curve 4 in FIG. 1.3, the SNR curve decreases at a small signal section, while the dynamic range expands.

Embodiment 5.1 Two-Stage Logarithmic Chain DAC

A resistor chain and a reference potential chain of the DAC are in a logarithmic relation. The logarithm law digital signals received by the DAC are high bit D_(q−1)˜D₀, and low bit D′_(t−1)˜D′₀. The high bit D_(q−1)˜D₀ are correspondently sent into control terminals d_(q−1)˜d₀ of a first-stage multi-channel switch, so as to generate a first-stage stage-potential V_(G). The low bit D′_(t−1)˜D′₀ are correspondently sent into control terminals d′_(t−1)˜d′₀ of a second-stage multi-channel switch, so as to generate a second-stage stage-potential V′_(B). Let b equal to some point within (0˜T−1), V′_(b) is called a reference potential point at second-stage step b, wherein a strobe potential point is the second-stage stage-potential V′_(B). According to Embodiment 5.1 of the present invention, the two-stage logarithmic chain DAC comprises a lossless switch.

LDA#_(β) comprises DZL_(β), JDWKG′ and Σ_(βU). DZL_(β), a second-stage logarithmic resistor chain, comprises a second-stage logarithmic resistor chain R′_(T)˜R′₁, and second-stage logarithmic reference potential points V′_(T−1)˜V′₀. The second-stage resistor chain is logarithmically provided as illustrated in Embodiment 4.1 of the present invention.

The second-stage resistor chain forms the T reference potential points V′_(T−1), V′_(T−2), . . . , V′₁, V′₀, and quantization intervals thereof (V′₁−0]→V′₀, (V′₂˜V′₁]→V′₁, (V′₃˜V′₂]→V′₂, . . . , (V′_(T−1)˜V′_(T−2)]→V′_(T−2), (V′_(T)˜V′T⁻¹]→V′_(T−1). A quantization step, or a step difference of V′_(b), ΔV′_(b)=V′_(b+1)−V′_(b). After the control terminals d′_(t−1)˜d′₀ of the second-stage stage-potential switch JDWKG′ receive the low bit digital signals D′_(t−1)˜D′₀, a strobe point S′_(b) is determined among second-stage switch points S′_(T−1)˜S′₀ and specially marked as S′_(B). The potential point V′_(b) correspondent to the strobe point S′_(B) is a second-stage stage-potential V_(βB). The second-stage stage-potential V_(βB) ranges within the T potential points V′₀, V′₁, . . . , V′_(T−2), V′_(T−1) whose quantization intervals respectively are: (V′₁˜V′₀]→V′₀, (V′₂˜V′₁]→V′₁, (V′₃˜V′₂]→V′₂, . . . , (V′_(T−1)˜V′_(T−2)]→V′_(T−2), (V′_(T)˜V′_(T−1)]→V′_(T−1), so an analog voltage correspondent to the second-stage stage-potential V_(βB) ranges within 0˜V_(P).

LDA#_(α) comprises DZL_(α), SJQH, JDWKG, and Σ_(AU). DZL_(α), a first-stage logarithmic resistor chain, comprises a first-stage logarithmic resistor chain R_(Q)˜R₁ and R_(θ), and first-stage logarithmic reference potential points V_(Q−1)˜V_(θ). The first-stage resistor chain is logarithmically provided as illustrated in the Embodiment 4.1 of the present invention. Let g be an arbitrary one of 0˜(Q−1), each first-stage-potential point V_(g) is correspondently connected to an summator Σ_(g), an attenuator Ψ_(g) and a switch point S_(g), so as to form a branch g. The voltage between the potential point V_(g) and the potential point V_(g+1) is called a step difference ΔV_(g) of the potential point V_(g), wherein ΔV_(g)=V_(g+1)−V_(g).

As the residue voltage of the stage-potential V_(G), the second-stage stage-potential V_(βB) is summed with the first-stage stage-potential V_(G). It is worth to mention that the analog voltage correspondent to the second-stage stage-potential V_(βB) ranges within 0˜V_(P), but the analog voltage is supposed to reasonably range within 0˜ΔV_(G). Thus, correspondent to the potential at step g, the range 0˜V_(P) of V_(βB) needs to be attenuated into 0˜ΔV_(g), which requires the attenuator Ψ_(g). It is also worth to mention that ΔV_(g) at each step is unequal, but geometric. Thus an attenuation coefficient ψ_(g) in lower case of the attenuator Ψ_(g) in upper case at each step are also geometric. Let ψ_(g)=ΔV_(g)/V_(P), the second-stage stage-potential V_(βB) is changed into an attenuated value V_(Ψg) based on an attenuation calculation of V_(Ψg)=V_(βB)*ψ_(g)=V_(βB)*ΔV_(g)/V_(P), in such a manner that the voltage range 0˜V_(P) of V_(βB) is attenuated into the range 0˜ΔV_(g) of V_(Ψg). V_(Ψg) is the residue voltage at step g of the first-stage reference potential points V_(Q−1)˜V_(θ) before becoming the strobe point. The first-stage reference potential V_(g) is a rough analog value, while the correspondent attenuated voltage V_(Ψg) as the residue voltage of V_(g) is a fine analog value. V_(g) is summed with V_(Ψg) through the summator Σ_(g), so as to generate a sum of the first-stage rough analog value V_(g) and the second-stage fine analog value V_(Ψg). The sum thereof is called a reference potential sum value V_(Σg). Each first-stage reference potential V_(g) has a correspondent reference potential sum value V_(Σg) to be outputted. After the control terminals d_(q−1)˜d₀ of the first-stage stage-potential switch JDWKG receive the high bit digital signals D_(q−1)˜D₀, a first-stage strobe point S_(G) is determined, and then the reference potential sum value V_(Σg) correspondent to the first-stage strobe point is outputted as a stage-potential sum value V_(ΣG) into a collector Σ_(αU). Actually, the collector Σ_(αU) only receives the single stage-potential sum value U_(ΣG) which is outputted in a form of a DA conversion value U_(αβ). Herein, the two-stage logarithmic chain DAC finishes the conversion.

It is puzzling to calculate the anti-logarithm through the logarithm chain. However, the analog signal is converted into the digital signal through the logarithm chain, and then the intact digital signal is converted through identically structured logarithm chain and naturally recovers into the original analog signal. For example, U_(αy)=V′₃ is converted by the logarithm chain ADC into D₂D₁D₀=000 and D′₃D′₂D′₁D′₀=0011; then D₂D₁D₀ and D′₃D′₂D′₁D′₀ are recovered by the logarithm chain DAC into V′₃. Actually, a reverse of logarithm-anti-logarithm is accomplished through a reverse of AD-DA.

Embodiment 5.2 Two-Stage Logarithmic Chain DAC with Half-Step Quantization Points

Based on Embodiment 5.1 of the present invention, the DAC of Embodiment 5.2 further comprises a half-step quantization of the reference potential points. According to Embodiment 5.2 of the present invention, the reference potential points of the DAC are the half-step quantization points as illustrated in the theoretical analysis. Half-step reference points are formed by moving all of the reference potential points a half step up; half-step resistance are formed by moving all of the resistance the half step up; U_(g) represents a first-stage half-step reference point; P_(g) represents a first-stage half-step resistance; U′_(b) represents a second-stage half-step reference point; P′_(b) represents a second-stage half-step resistance. A correspondence between a resistor chain of the DAC in Embodiment 5.2 and the resistor chain of the DAC in Embodiment 5.1 is U_(g)→V_(g), P_(g)→R_(g), U′_(b)→V′_(b), P′_(b)→R′_(b). The half-step means moving the original reference potential points the half step up, calculated as follows.

Moving all the reference potential points the half step up generates the first-stage half-step reference point U_(g)=(V_(g)+V_(g)*η)/2, the first-stage half-step resistance P_(g)=(R_(g)+R_(g)*η)/2, the second-stage half-step reference points U′_(b)=(V′_(b)+V′_(b)*η)/2, and the second-stage half-step resistance P′_(b)=(R′_(b)+R′_(b)*η)/2, so as to accomplish moving all of the reference potential points and the resistance the half step up.

Through the half-step processing, the two-stage logarithmic chain DAC is changed into the two-stage logarithmic chain DAC with the half-step quantization points. After the half-step processing of the reference potential points, the quantization step is shortened by a half, which decreases a quantization error by ¾ and increase [S_(j)/N_(j)]_(dB) by 10 log 4=6.02 dB.

Embodiment 6.1 Digital Logarithmic Converter

A linear analog signal is firstly converted into an N-bit logarithm law digital signal by the two-stage N-bit logarithmic chain ADC as illustrated in Embodiment 4.1, and then converted into an output analog signal by a N-bit linear DAC. The output analog signal is an analog signal based on a logarithm law.

Embodiment 6.2 Digital Anti-Logarithmic Converter

An analog signal based on a logarithm law is firstly converted into an N-bit logarithm law digital signal by an N-bit linear ADC, and then converted into an output analog signal by an N-bit two-stage logarithmic chain DAC. The output analog signal is a linear analog signal. The N-bit two-stage logarithmic chain DAC is as illustrated in Embodiment 5.1 of the present invention.

Embodiment 7.1 Logarithm Chain ADC Having at Least Three Sub-Stages

Similar to the two-stage logarithm chain ADC, the logarithm chain ADC having at least three sub-stages comprises the second sub-stage as the final stage, and further comprises one or more than one intermediate sub-stage which has an identical structure to the first sub-stage, such as a first intermediate sub-stage, a second intermediate sub-stage and a third intermediate sub-stage.

Embodiment 7.2 Logarithm Chain DAC Having at Least Three Sub-Stages

Similar to the two-stage logarithm chain DAC, the logarithm chain DAC having at least three sub-stages further comprises at least one added sub-stage which is identical to the second sub-stage. The added sub-stage comprises a resistor chain, a stage-potential switch and a correspondent attenuator group.

One skilled in the art will understand that the embodiment of the present invention as shown in the drawings and described above is exemplary only and not intended to be limiting.

It will thus be seen that the objects of the present invention have been fully and effectively accomplished. Its embodiments have been shown and described for the purposes of illustrating the functional and structural principles of the present invention and is subject to change without departure from such principles. Therefore, this invention includes all modifications encompassed within the spirit and scope of the following claims. 

What is claimed is:
 1. Multi-stage parallel super-high-speed ADC and DAC of a logarithmic companding law, wherein the logarithmic ADDA comprises multi-sub-ADDAs, wherein at least one sub-ADDA comprises a stage-potential processing device, wherein the stage-potential processing device at stage λ comprising: a stage-potential generating module at stage λ which comprises a resistor chain for generating reference potential points and a potential stage determining circuit, wherein let Q=2^(q), the q-bit reference potential points of the sub-ADDA at stage λ are formed by series connected Q resistors; the resistor chain of the series connected Q resistors provides Q+1 potential points V_(λQ), V_(λ(Q−1)) . . . V_(λ1), V_(λ0), among which V_(λ(Q−1)) . . . V_(λ1), V_(λ0) are the Q step reference potential points at stage λ, wherein V_(λQ) is equal to a power source anode V_(p), and is excluded from the reference potential at step Q; let g be equal to some point whose subscript is within (0˜Q−1), point g is called a test point, and V_(λg) is the reference potential at step g stage λ; a quantization distance (also called a step difference) Δ_(λg)=V_(λ(g+1))−V_(λg); when a to-be-compared voltage U_(λZ) falls within a conversion range V_(λQ)˜0, there is always a point G correspondent to U_(λZ), wherein, when g=G, V_(λ(G+1))>U_(λZ)>V_(λG) and U_(λZ)−V_(λG)<Δ_(λG); particularly, point G is named as a stage point, and V_(λg) at the stage point G is the reference point which is smaller than and closest to U_(λZ); V_(λg) is a special reference point among the reference points V_(λ(Q−1))−V_(λ0), especially marked as V_(λG); V_(λG) is called a stage-potential at stage λ; relative to the sub-ADDA at stage λ, the stage-potential V_(λG) is a conversion value of U_(λZ); a stage-potential extracting module, wherein, for the sub-ADDA at stage λ, although it can be determined that which of the reference potential points V_(λ(Q−1))˜V_(λ0) is the stage-potential V_(λG), the stage-potential V_(λG) still remains to be extracted, which requires the stage-potential extracting module; the stage-potential extracting module is a stage-potential switch; a group of threshold switches forms the stage-potential switch; the stage-potential switch JDWKG_(λ) comprises a threshold switch group LJKGZ_(λ) and a multi-channel switch DLKG_(λ), wherein the threshold switch group is the group of the threshold switches whose output terminals are parallel connected into a common terminal and whose input terminals form an input terminal group of the threshold switch group; control characters are provided for directly choosing and connecting one of the input terminals as a strobe terminal; the threshold switch point S_(λg) at step g stage λ has an upper control character I_(λ(g+1)) and a lower control character I_(λg) which are respectively connected to and equal to potential comparison values I*_(λ(g+1)) and I*_(λg); when I_(λ(g+1))=1 or I_(λg)=0, the switch point S_(λg) is open; only when the switch point S_(λg) satisfies requirements of I_(λ(g+1))=0 and I_(λg)=1, the switch point S_(λg) is connected and becomes a strobe point S_(λG); a potential at the strobe point S_(λG) is V_(λG) at step G stage λ, and is also called the stage-potential V_(λG) of stage λ; wherein the stage-potential V_(λG) is a bridge of A/D conversion and D/A conversion, and corresponds respectively to digital signals D_(λ(q−1))˜D_(λ0) and the to-be-compared voltage U_(λZ), wherein the correspondence is accomplished via a correspondence between the reference points V_(λ(Q−1))˜V_(λ0) and the control characters I_(λ(Q−1))˜I_(λ0), and a correspondence between the reference points V_(λ(Q−1))˜V_(λ0) and the threshold switch group S_(λ(Q−1))˜S_(λ0); the stage-potential V_(λG) is a threshold point among the reference points V_(λ(Q−1))˜V_(λ0), and is determined through values of the control characters I_(λ(Q−1))˜I_(λ0) and the strobe terminal of the threshold switch group S_(λ(Q−1))˜S_(λ0); wherein the stage-potential V_(λG) is obtained through the correspondence between the reference points V_(λ(Q−1))˜V_(λ0) and the control characters I_(λ(Q−1))˜I_(λ0), and the correspondence between the reference points V_(λ(Q−1))˜V_(λ0) and the switch group S_(λ(Q−1))˜S_(λ0); wherein firstly, the correspondence between V_(λ(Q−1))˜V_(λ0) and the digital signals, or the correspondence between V_(λ(Q−1))˜V_(λ0) and the control characters I_(λ(Q−1))˜I_(λ0) is illustrated as follows; among the reference points V_(λ(Q−1))˜V_(λ0), V_(λG) is the threshold point, when the to-be-compared voltage at stage λ U_(λZ)>(V_(λG)˜V_(λ0)), the control characters I_(λG)˜I_(λ0) correspondent to the reference points V_(λG)˜V_(λ0) are equal to 1; in other words, each threshold switch (S_(λ(G−1))˜S_(λ0)) connected below V_(λG) has the control character I_(λ(g+1))=I_(λg)=1, so (S_(λ(G−1))˜S_(λ0)) are at states of OFF; when U_(λz)<(V_(λQ)˜V_(λ(G+1))), the control characters I_(λQ)˜I_(λ(G+1)) correspondent to the reference points V_(λQ)˜V_(λ(G+1)) are equal to zero; in other words, each threshold switch (S_(λ(G+1))˜S_(λ(Q−1))) connected above V_(λG) has the control character I_(λ(g+1))=I_(λg)=0, so (S_(λ(G+1))˜S_(λ(Q−1))) are also at states of OFF; only when the threshold switch S_(λG) at the threshold point has the control characters I_(λ(G+1))=0 and I_(λG)=1, S_(λG) is at a state of ON; and secondly, V_(λ(Q−1))˜V_(λ0) and the correspondent S_(λ(Q−1))˜S_(λ0) are connected directly, or correspondently via an arithmetic circuit; the strobe point S_(λG) among S_(λ(Q−1))˜S_(λ0) extracts out the stage-potential V_(λG), and sends the extracted stage-potential V_(λG) into a main line S_(λ) of the stage-potential switch; the sent stage-potential V_(λG) and the stage output values of other sub-ADDAs are collected and calculated, for accomplishing the A/D and D/A conversions; the stage-potential V_(λG) is the reference point potential closest to the to-be-compared voltage U_(λZ); V_(λG) and U_(λZ) have a relation of V_(λG)=U_(λZ)−U_(λx), wherein U_(λx) is a residue voltage which is smaller than a span of the reference point voltage; and wherein the threshold switch comprises a lossy switch and a lossless switch, wherein the lossless switch comprises a voltage follower switch which functions as a signal switch for transmitting or blocking signals, wherein the voltage follower switch comprises two modules, a module of a voltage follower and a module of a power source switch; the power source switch is an electronic device provided on a power source loop of the follower; connection and disconnection of the power source loop of the follower are controlled by the power source switch through the control characters, so as to control connection and disconnection of a signal loop of the follower.
 2. A lossless switch based on a follower switch, wherein the follower switch of the lossless switch functions as a signal switch for transmitting or blocking signals; the follower switch comprises two modules, a follower and a power source switch, wherein the power source switch is an electronic device provided on a power source loop of the follower, and controls connection and disconnection of the power source loop of the follower through control characters; and wherein the follower is at a state of following voltage when the power source loop is connected; herein the signal is inputted through a non-inverting terminal of the follower, and a voltage of an output terminal is accurately equal to a voltage of the non-inverting terminal, in such a manner that the signal is on; the follower cuts off the signal when the power source loop is disconnected; the follower switch controls the connection and disconnection of the power source loop through the control characters, so as to further control connection and disconnection of a signal loop of the follower; logic relations about the connection and disconnection of the follower switch formed by the control characters is arbitrary, comprising normally open, normally close and threshold switching; preferably, the follower switch is a threshold switch having the logic relations; the threshold switch S_(λg) comprises S_(λg1), S_(λg2) and S_(λg3).
 3. The lossless switch based on a follower switch, as recited in claim 2, wherein the lossless switch S_(λg) is transformed from the follower switch by establishing a control logic of the power source switch; the logic comprises: when I_(λg)=0 or I_(λ(g+1))=1, S_(λg) is signal off; only when I_(λg)=1 and I_(λ(g+1))=0, A_(λg) is powered on only by closing KS1 and KS3 which are power source switches conducting at high potential and closing KS0 and KS2 which are power source switches conducting at low potential, in such manner that A_(λg) is signal on; otherwise, once I_(λg)=0 or I_(λ(g+1))=1, KS1 and KS3 are cutting off, or, KS0 and KS2 are cutting off, in such a manner that A_(λg) is powered off and thus signal-off; for simplification, one of KS0 and KS2 is arbitrarily in short circuit; one of KS1 and KS3 is arbitrarily in short circuit.
 4. The multi-stage parallel super-high-speed ADC and DAC of the logarithmic companding law, as recited in claim 1, wherein an m stages*q-bit equal resistance logarithmic ADC is established as follows, wherein after being processed by a front-end circuit QZDL, an original input alternating signal u_(αy) becomes an input voltage at stage α U_(αy); an input voltage U_(λy) at stage λ ranges between 0˜V_(p); AD#_(λ) at stage λ processes the input voltage U_(λy) at stage λ with an AD conversion through following five modules and processes thereof: (1) a stage-potential V_(λG) generating module, wherein, let Q=2^(q), a voltage-dividing resistor chain of a parallelizer at stage λ R_(λ(Q−1))˜R_(λ0) forms potential reference points V_(λ(Q−1))˜V_(λ0) at stage λ, wherein V_(λ0) is a bottom potential; the reference points V_(λ(Q−1))˜V_(λ1) are correspondently connected to inverting terminals of comparators C_(λ(Q−1))˜C_(λ1) in the parallelizer; the input voltage at stage λ U_(λy) becomes a temporarily stable voltage U*_(λy) through sampling and holding; then summing the bottom potential V_(λ0) and the temporarily stable voltage U*_(λy) forms a to-be-compared voltage U_(λZ); the to-be-compared voltage U_(λZ) is connected to non-inverting terminals of the comparators C_(λ(Q−1))˜C_(λ1), and compared with the potential reference points V_(λ(Q−1))˜V_(λ0), so as to generate the stage-potential V_(λG); through V_(λ(G+1))>U_(λZ)>V_(λG), a threshold point G of comparison values I_(λ(Q−1))˜I_(λ1) at stage λ satisfying requirements of I_(λ(Q−1))˜I_(λ(G+1))=0 and I_(λG)˜I_(λ1)=1 is determined; let I_(λQ) constantly 0 and I_(λ0) constantly 1, the comparison values I_(λ(Q−1))˜I_(λ0) are encoded by an encoder BM_(λ), and then digital output values D_(λ(q−1))˜D_(λ0) of the stage-potential V_(λG) are obtained; herein, with the stage-potential V_(λG) as a bridge, the to-be-compared U_(λZ) is converted into the stage-potential V_(λG) and further into the digital signals D_(λ(q−1))˜D_(λ0); (2) a switch error reducing module which reduces switch errors by applying identical elevation to the potential of the reference points and the input voltage, or through a lossless switch; (3) a stage-potential V_(λG) extracting module, wherein all sub-stages in AD## needs to extract out the stage-potential V_(λG) for a preparation of the conversion at next sub-stage, except the final sub-stage; the stage-potential is extracted for the conversion at next sub-stage; given that a conversion bit number of each sub-stage is q, Q=2^(q), the voltage V_(p) is divided by the resistor chain into Q equal voltages ΔV; each ΔV is a fixed value ΔV=V_(p)/Q; the reference potential points V_(λ(Q−1))˜V_(λ0) are arithmetically connected to the switch points S_(λ(Q−1))˜S_(λ0) one by one; a strobe point S_(λG) is determined through a strobe control of the threshold switch group; the strobe point S_(λG) corresponds to the stage-potential V_(λG), and sends the stage-potential V_(λG) into a switch main line S_(λ); (4) an inter-stage operation module, comprising a sampler/holder CB_(λ), a residue summator Σ_(λ) and a residue amplifier FD_(λ), wherein the input voltage U_(λy) at stage λ becomes the stable U*_(λy) through the sampler/holder CB_(λ), in such a manner that the m sub-stages are able to run parallel; the residue summator Σ_(λ) generates a residue voltage U_(λX)=U_(λZ)−V′_(λG)−V_(λS); the residue voltage U_(λx) is within 0˜ΔV; the residue amplifier FD_(λ) amplifies a residue voltage signal Q times, so as to generate U_((λ+1)y)=U_(μy)=Q*U_(λx); as a result, a range of U_(μy) expands into a full scale of 0˜V_(p), and U_(μy) becomes the input voltage at stage μ; the input voltage U_(μy) at stage μ enters AD#_(μ) at stage μ for measurement and conversion at a higher accuracy; and (5) a logarithmic conversion module and a process thereof comprising an analog conversion and a digital conversion, wherein the digital conversion is based on converting an overall input voltage Uαy into high-bit digital signals having equal quantization distances, and then converting the high-bit digital signals into low-bit digital signals having logarithmic quantization distances through a logarithm table; the analog conversion is based on converting a linear input voltage into the logarithmic input voltage through an analog logarithm converter before inputting into stage α, while actually ADC is for converting the logarithmic input voltage into the digital signals having the logarithmic quantization distances.
 5. The multi-stage parallel super-high-speed ADC and DAC of the logarithmic companding law, as recited in claim 1, wherein an m stages*q-bit equal resistance logarithmic DAC is established as follows, wherein N-bit digital signals are allocated as m stages*q-bit: (D_((N−1))), . . . , D₀)=(D_(α(q−1)), . . . , D_(α0)), (D_(β(q−1)), . . . , D_(β0)), . . . , (D_(m(q−1)), . . . , D_(m0)); D are sent into control terminals of correspondent stage-potential switches: (d_(α(q−1)), . . . , d_(α0)), (d_(β(q−1)), . . . , d_(β0)), . . . , (d_(m(q−1)), . . . , d_(m0)); the sub-DAC_(λ) at stage λ processes the digital signals at stage λ (D_(λ(q−1)), . . . , D_(λ0)) with a DA conversion through following four modules and processes thereof: (1) a stage-potential V_(λG) generating module, wherein Q=2^(q); a voltage-dividing resistor chain R_(λQ)˜R_(λ0) of a parallelizer at stage λ forms potential reference points V_(λ(Q−1))˜V_(λ0) at stage λ; after the stage-potential V_(λG) generating module receives the digital signals (D_(λ(q−1)), . . . , D_(λ0)), the reference potential point V_(λG) correspondent to the digital signals becomes a stage-potential; V_(λ0) is a bottom potential; (2) a switch error reducing module, identical to the switch error reducing module of Embodiment 2.1; (3) a stage-potential V_(λG) extracting module, wherein the stage-potential V_(λG) of each stage needs to be extracted out for calculating an output voltage V_(λΨ) of each stage; the stage-potential V_(λG) extracting module and a process thereof are identical to the stage-potential V_(λG) extracting module and process in Embodiment 2.1; (4) an inter-stage operational module, wherein the stage-potential V_(λG), the output voltage V_(λΨ) and an attenuation coefficient Ψ_(λ) have a relation of: V_(λΨ)=V_(λG)/Ψ_(λ), wherein Ψ_(λ)=Q^((λ−1)), namely an attenuation coefficient of an attenuator Ψ_(λ) at stage λ is Ψ_(λ)=Q^((λ−1)); a summation of V_(λΨ) of all stages is executed by an overall summator Σ_(Ψ), so as to generate an overall output analog voltage V_(Ψ); through the attenuator and the overall summator, the bottom potential of each stage becomes equal to a constant V_(RS): V_(RS)=V_(α0)/Ψ_(α)+V_(β0)/Ψ_(β)+ . . . +V_(m0)/Ψ_(m)=V_(α0)/(Q^(m−α))+V_(β0)/(Q^(m−β))+ . . . +V_(m0)/(Q^(m−m)); a waveform of the overall output analog voltage V_(Ψ) is only elevated by V_(RS), without being transformed; the waveform of the overall output analog voltage V_(Ψ) is obtained by subtracting V_(RS) in the overall summator Σ_(Ψ); and (5) a logarithmic conversion module comprising an analog conversion module and a digital conversion module, wherein the digital conversion module is based on, after receiving low-bit digital signals having logarithmic quantization distances, converting the digital signals into high-bit digital signals having equal quantization distances through an anti-logarithm table, and then converting the high-bit digital signals into analog signals by a high-bit DAC having equal quantization distances; the analog conversion module is based on, after accomplishing the DA conversion by the DAC, converting the logarithmic analog signals into a linear output voltage by an analog anti-logarithmic converter.
 6. The multi-stage parallel super-high-speed ADC and DAC of the logarithmic companding law, as recited in claim 1, wherein a two-stage logarithmic chain ADC is establish as follows; the logarithmic chain ADC comprises two sub-stages, LAD#_(α) and LAD#_(β); LAD#_(α) is a first-stage logarithmic chain sub-ADC, and LAD#_(β) is a second-stage logarithmic chain sub-ADC; the two-stage logarithmic chain ADC further comprises a lossless switch; wherein the first-stage LAD#_(α) executes a q-bit conversion; a logarithm law resistor chain R_(Q)˜R₁ and R_(θ) divides a voltage 0˜V_(P) into Q+1 segments, forming Q+2 potential points; except 0 and V_(P), V_(Q−1)˜V_(θ) are reference potential points, or quantized points, which have Q=2^(q) steps; the reference potential chain V_(Q−1)˜V_(θ) are set based on the logarithm law; V_(Q−1)˜V₁ are connected to inverting terminals of correspondent first-stage comparators C_(Q−1)˜C₁, and a first-stage to-be-compared voltage U_(αZ) is connected to non-inverting terminals of each first-stage comparator, so as to generate first-stage comparison values I_(Q−1)˜I₁; through encoding the first-stage comparison values by a first-stage encoder BM, first-stage logarithmic digital output signals D_(q−1)˜D₀ are generated; a stage-potential V_(G) of the to-be-compared voltage U_(αZ) is obtained by controlling a stage-potential switch JDWKG via the first-stage comparison values I_(Q−1)˜I₁ or the digital output signals D_(q−1)˜D₀, namely obtaining a rough result of U_(αZ) about a detection that to which segments of the first-stage-potential chains the to-be-compared voltage U_(αZ) belongs; the to-be-compared voltage U_(αZ) is connected to first-stage summators Σ_(Q−1)˜Σ₀ to be a minuend, and the reference potential points V_(Q−1)˜V_(θ) are correspondently connected to Σ_(Q−1)˜Σ₀ to be subtrahends, so as to generated difference voltages U_(X(Q−1))˜U_(X0); then, the difference voltages U_(X(Q−1))˜U_(X0) are sent into first-stage amplifiers F_(Q−1)˜F₀ to generate operational voltages U_(y(Q−1))˜U_(y0); the difference voltage correspondent to the stage-potential V_(G) is called a residue voltage U_(XG); the operational voltage correspondent to the stage-potential V_(G) is called an operational stage-potential U_(yG); the summators acquires that the residue voltage U_(XG)=U_(αZ)−V_(G) and that U_(XG) ranges within (0˜ΔV_(G)), wherein ΔV_(G) is a quantization distance of the stage-potential; ΔV_(G)=(V_((G+1))−V_(G)); let an amplification coefficient of the amplifier F_(G) be V_(p)/ΔV_(G), the amplifier F_(G) generates the operational stage voltage U_(yG)=U_(XG)*V_(p)/ΔV_(G); after U_(XG) is amplified into U_(yG), the voltage range expands into a full scale of 0˜V_(p); the stage-potential switch extracts out the operational stage voltage U_(yG) and sends the extracted U_(yG) into a switch main line S_(α) towards the next stage; U_(yG) becomes the to-be-compared voltage at the next stage U_(βZ) after being sampled and held by a sampler/holder CB_(β), before an accurate measurement at the next stage; the input voltages of the two sub-stages maintain independent and stable within a sampling cycle due to the inter-stage sampler/holder CB_(β), in such a manner that the two sub-stages are capable of parallel operating and forming a pipeline type conversion; the second-stage LAD#_(β) mainly comprises a second-stage logarithmic chain parallelizer LBXQ_(β), wherein second-stage logarithmic resistor chain R′_(T)˜R′₁ form potential points V_(P) and V′_(T−1)˜V′₀; except V_(p), V′_(T−1)˜V′₀ are second-stage logarithmic reference potential points; V′_(T−1)˜V′₁ are connected to correspondent inverting terminals of second-stage comparators C′_(T−1)˜C′₁, and the second-stage to-be-compared voltage U_(βZ) is connected to a non-inverting terminal of each second-stage comparator, so as to generate second-stage comparison values I′_(T−1)˜I′₁; then the second-stage comparison values I′_(T−1)˜I′₁ are encoded by a second-stage encoder BM′ to generate second-stage logarithm law digital signals D′_(t−1)˜D′₀; the two sub-stages, LAD#_(α) and LAD#_(β), together accomplish the digital signals conversion of the q+t bits logarithm law, wherein D_(q−1)˜D₀ are high bit and D′_(t−1)˜D′₀ are low bit; the logarithmic resistor chain is for increasing an SNR and broadening a signal dynamic range; the resistor chains of the two sub-stages, LAD#_(α) and LAD#_(β) are set according to the logarithm law as follows; the first-stage resistor chain is logarithmically provided, wherein the resistor chain of LAD#_(α) has a constant resistance, so a chain current I_(α) is also constant; let a base potential V_(θ) be equal to a minimum effective detection value of a sensor, and let a base resistance R_(θ)=V_(θ)/I_(α) and R_(A)/R_(θ)=η−1, wherein R_(A) is a virtual start resistance, the first-stage chain resistances successively increase by a large ratio of η^(T) from R_(A), which forms a large ratio resistor chain: R₁=R_(A)*η^(T), R₂=R_(A)*η²*^(T), . . . , R_(Q−3)=R_(A)*η^((Q−3))*^(T), R_(Q−2)=R_(A)*η^((Q−2))*^(T), R_(Q−1)=R_(A)*η^((Q−1))*^(T); the large ratio resistor chain R_(θ)˜R_(Q) forms a large ratio potential chain (V_(j+1)/V_(j)=η^(T)): ground, V_(η), V₁=V_(θ)*η^(T), V₂=V_(θ)*η²*^(T), V₃=V_(θ)*η³*^(T), . . . , V_(Q−2)=V_(θ)*η^((Q−2))*^(T), V_(Q−1)=V_(θ)*η^((Q−1))*^(T), V_(Q)=V_(θ)*η^(Q)*^(T)=V_(p); except point V_(Q)=V_(P), totally Q reference potential points, also called quantized points, are: V_(θ), V₁, . . . , V_(Q−1); because a region below V_(θ) is an invalid detection region of the sensor, V_(θ) is the quantized point of the region of (V₁˜V_(θ)˜0) which is marked as (V₁˜V_(θ)˜0)→V_(θ); quantization intervals of the other quantized points are: (V₂˜V₁]→V₁, (V₃˜V₂]→V₂, . . . , (V_(Q−1)˜V_(Q−2)]→V_(Q−2), (V_(Q)˜V_(Q−1)]→V_(Q−1); since the first-stage quantized points are rough because of the large ratio η^(T), it is necessary to insert T second-stage fine quantized points having a small ratio of 71 therebetween; the second-stage resistor chain is logarithmically provided; the resistor chain of LAD#_(β) comprises T=2^(t) resistors R′₁˜R′_(T); at the first stage, the residue voltage U_(XG)=U_(αZ)−V_(G) ranges within (0˜ΔV_(G)); ΔV_(G)=(V_((G+1))−V_(G)); V_(G)=V_(θ)*η^(G)*^(T), V_((G+1))=V_(θ)*η^((G+1))*^(T), wherein ΔV_(G) is the quantization step of the first-stage stage-potential V_(G); theoretically, T fine quantized points of the second sub-stage need to be inserted into V_(G)˜V_((G+1)); the fine quantized points of V_(G)˜V_((G+1)) comprise V″₀=V_(G)=V_(θ)*η^(G)*^(T), V″₁=V_(G)*η¹, V″₂=V_(G)*η², V″₃=V_(G)*η³, . . . , V″_(T−2)=V_(G)*η^(T−2), V″_(T−1)=V_(G)*η^(T−1), wherein the fine quantized points increase geometrically by a ratio of η; thus, once the second-stage resistor chain has the geometrical relation of η and is multiplied by a coefficient, the second-stage resistor chain is capable of accomplishing the logarithmic conversion of the residue voltage; actually, the second-stage conversion is extracting out the first-stage residue voltage U_(XG), rather than inserting the fine quantized points into V_(G)˜V_((G+1)); U_(XG) ranges within (0˜ΔV_(G)); the first-stage residue voltage U_(XG) expands into the first-stage operational stage voltage U_(yG) after being amplified by the correspondent amplifier F_(G); let the amplification coefficient of the amplifier F_(G) be V_(P)/ΔV_(G), U_(yG)=U_(XG)*V_(P)/ΔV_(G), and the range of (0˜ΔV_(G)) is expanded into a second-stage full scale of 0˜V_(p); the operational stage-potential U_(yG) becomes the second-stage to-be-compared voltage U_(βZ) after being sampled and held by the sampler/holder CB_(β); it is a key of the second-stage resistor chain to establish the logarithm law quantized points; in the second-stage resistor chain, given that R_(B) is an arbitrary virtual resistance, values of T chain resistors increase geometrically by the ratio of η: R′₁=R_(B)*η¹, R′₂=R_(B)*η², R′₃=R_(B)*η³, . . . , R′_(T−2)=R_(B)*η^(T−2), R′_(T−1)=R_(B)*η^(T−1), R′_(T)=R_(B)*η^(T), and then naturally T quantized points whose potentials geometrically increase by the ratio of η are formed: 0, V′₁=V_(B)*η¹, V′₂=V_(B)*η², V′₃=V_(B)*η³, . . . , V′_(T−2)=V_(B)*η^((T−2)), V′_(T−1)=V_(B)*η^((T−1)), as well as the quantization intervals thereof: (V′₁˜0]→0, (V′₂˜V′₁]→V′₁, (V′₃˜V′₂]→V′₂, . . . , (V′_(T−1)˜V′_(T−2)]→V′_(T−2), (V′_(T)˜V′^(T−1)]→V′^(T−1); V′T=V_(P) is excluded from the second-stage quantized points; and herein, the logarithmic ADC with two resistor chains of the two sub-stages convert the analog signals into the logarithmic digital signals having a constant SNR; further, if the base resistance R_(θ) is adjusted into an adjustment resistance R*_(θ), wherein R*_(θ)=R_(θ)˜R_(θ)/15, let R*_(θ) be the minimal effective signal of the sensor, by reducing the adjustment resistance R*_(θ), the SNR curve decreases at a small signal terminal, and the dynamic range expands.
 7. The multi-stage parallel super-high-speed ADC and DAC of the logarithmic companding law, as recited in claim 1, wherein a two-stage logarithmic chain DAC is establish as follows; the two-stage logarithmic chain DAC comprises a resistor chain and a reference potential chain which are in a logarithmic relation; the DAC receives logarithm law digital signals comprising high bit D_(q−1)˜D₀, and low bit D′_(t−1)˜D′₀, wherein the high bit D_(q−1)˜D₀ are correspondently sent into control terminals d_(q−1)˜d₀ of a first-stage multi-channel switch, so as to generate a first-stage stage-potential V_(G); and the low bit D′_(t−1)˜D′₀ are correspondently sent into control terminals d′_(t−1)˜d′₀ of a second-stage multi-channel switch, so as to generate a second-stage stage-potential V′_(B); let b equal to some point within (0˜T−1), V′_(b) is called a reference potential point at second-stage step b, wherein a strobe potential point is the second-stage stage-potential V′_(B); the two-stage logarithmic chain DAC further comprises a lossless switch; LDA#_(β) comprises DZL_(β), JDWKG′ and Σ_(βU); DZL_(β), a second-stage logarithmic resistor chain, comprises a second-stage logarithmic resistor chain R′_(T)˜R′₁, and second-stage logarithmic reference potential points V′_(T−1)˜V′₀; the second-stage resistor chain is logarithmically provided as illustrated in Embodiment 4.1 of the present invention; the second-stage resistor chain forms the T reference potential points V′_(T−1); V′_(T−2), . . . , V′₁, V′₀, and quantization intervals thereof (V′₁˜0]→>V′₀, (V′₂˜V′₁]→V′₁, (V′₃˜V′₂]→V′₂, . . . , (V′_(T−1)˜V′_(T−2)]→V′_(T−2), (V′_(T)˜V′_(T−1)]→V′_(T−1); a quantization step, or a step difference, of V′_(b) is ΔV′_(b)=V′_(b+1)−V′_(b); after the control terminals d′_(t−1)˜d′₀ of the second-stage stage-potential switch JDWKG′ receive the low bit digital signals D′_(t−1)˜D′₀, a strobe point S′_(b) is determined among second-stage switch points S′_(T−1)˜S′₀ and specially marked as S′_(B); the potential point V′_(b) correspondent to the strobe point S′_(B) is a second-stage stage-potential V_(βB); the second-stage stage-potential V_(βB) ranges within the T potential points V′₀, V′₁, . . . , V′_(T−2), V′_(T−1) whose quantization intervals respectively are: (V′₁˜V′₀]→V′₀, (V′₂˜V′₁]→V′₁, (V′₃˜V′₂]→V′₂, . . . , (V′_(T−1)˜V′_(T−2)]→V′_(T−2), (V′_(T)˜V′_(T−1)]→V′_(T−1), so an analog voltage correspondent to the second-stage stage-potential V_(βB) ranges within 0˜V_(P); LDA#_(α) comprises DZL_(α), SJQH, JDWKG, and Σ_(AU); DZL_(α), a first-stage logarithmic resistor chain, comprises a first-stage logarithmic resistor chain R_(Q)˜R₁ and R_(θ), and first-stage logarithmic reference potential points V_(Q−1)˜V_(θ); the first-stage resistor chain is logarithmically provided; let g be an arbitrary one of 0˜(Q−1), each first-stage-potential point V_(g) is correspondently connected to an summator Σ_(g), an attenuator Ψ_(g) and a switch point S_(g), so as to form a branch g; the voltage between the potential point V_(g) and the potential point V_(g+1) is called a step difference ΔV_(g) of the potential point V_(g), wherein ΔV_(g)=V_(g+1)−V_(g); the second-stage stage-potential V_(βB) is summed with the first-stage stage-potential V_(G) as the residue voltage of the stage-potential V_(G); the range 0˜V_(P) of V_(βB) is attenuated into 0˜ΔV_(g) through the attenuator Ψ_(g); because ΔV_(g) at each step is unequal but geometric, an attenuation coefficient ψ_(g) of the attenuator Ψ_(g) at each step is also geometric; let ψ_(g)=ΔV_(g)/V_(P), the second-stage stage-potential V_(βB) is changed into an attenuated value V_(Ψg) based on an attenuation calculation of V_(Ψg)=V_(βB)*ψ_(g)=V_(βB)*ΔV_(g)/V_(P), in such a manner that the range 0˜V_(P) of V_(βB) is attenuated into the range 0˜ΔV_(g) of V_(Ψg); the attenuated voltage V_(Ψg) is the residue voltage at step g of the first-stage reference potential points V_(Q−1)˜V_(θ) before becoming the strobe potential; the first-stage reference potential V_(g) is a rough analog value, while the correspondent attenuated voltage V_(Ψg) as the residue voltage of V_(g) is a fine analog value; V_(g) is summed with V_(Ψg) through the summator Σ_(g), so as to generate a sum of the first-stage rough analog value V_(g) and the second-stage fine analog value V_(Ψg); the sum thereof is called a reference potential sum value V_(Σg); each first-stage reference potential V_(g) has a correspondent reference potential sum value V_(Σg) to be outputted; after the control terminals d_(q−1)˜d₀ of the first-stage stage-potential switch JDWKG receive the high bit digital signals D_(q−1)˜D₀, a first-stage strobe point S_(G) is determined, and then the reference potential sum value V_(Σg) correspondent to the first-stage strobe point is outputted as a stage-potential sum value U_(ΣG) into a collector Σ_(αU); actually, the collector Σ_(αU) only receives the single stage-potential sum value U_(ΣG) which is outputted in a form of a DA conversion value U_(αβ); herein, the two-stage logarithmic chain DAC finishes the conversion.
 8. The multi-stage parallel super-high-speed ADC and DAC of the logarithmic companding law, as recited in claim 1, wherein a two-stage logarithmic chain DAC having half-step quantization points is established, and reference potential points of the DAC are the half-step quantization points; half-step reference points are formed by moving all of the reference potential points a half step up; half-step resistances are formed by moving all of the resistances the half step up; U_(g) represents a first-stage half-step reference point; P_(g) represents a first-stage half-step resistance; U′_(b) represents a second-stage half-step reference point; P′_(b) represents a second-stage half-step resistance; a correspondence between a resistor chain of the DAC having the half-step quantization points and the resistor chain of the DAC is U_(g)→V_(g), P_(g)→R_(g), U′_(b)→V′_(b), P′_(b)→*R′_(b); the half-step means moving the original reference potential points the half step up, calculated as: moving all the reference potential points the half step up generates the first-stage half-step reference point U_(g)=(V_(g)+V_(g)*η)/2, the first-stage half-step resistance P_(g)=(R_(g)+R_(g)*η)/2, the second-stage half-step reference points U′_(b)=(V_(b)+V_(b)*η)/2, and the second-stage half-step resistance P′_(b)=(R′_(b)+R′_(b)*η)/2, so as to accomplish moving all of the reference potential points and the resistance the half step up.
 9. The multi-stage parallel super-high-speed ADC and DAC of the logarithmic companding law, as recited in claim 1, wherein a digital logarithmic converter is established, wherein a linear analog signal is firstly converted into an N-bit logarithm law digital signal by the two-stage N-bit logarithmic chain ADC, and then converted into an output analog signal by a N-bit linear DAC; and the output analog signal is an analog signal based on a logarithm law.
 10. The multi-stage parallel super-high-speed ADC and DAC of the logarithmic companding law, as recited in claim 1, wherein a digital anti-logarithmic converter is established, wherein an analog signal based on a logarithm law is firstly converted into an N-bit logarithm law digital signal by an N-bit linear ADC, and then converted into an output analog signal by an N-bit two-stage logarithmic chain DAC; and the output analog signal is a linear analog signal. 